Feel free to take any of these interpretations and Ideas for your own stories, I would love to read your works.
also understand I did not hold these notes to any quality standard of writing I simply wanted my ideas out on paper before I forgot.
Bakugou can cause explosions on his feet as well due to your feet having the same skin and sweat glands as your hands, it only makes sense that whatever ability using sweat glands on his hands would work on his feet, also whats stopping him from having explosions everywhere, its all of his sweat that is nitroglycerine, maybe he can and its just harder, perhaps he can but hes never tried?
he has mild super strength due to his body needing to withstand his explosions, along with enhanced durability for the same reason.
He has a mild healing factor to fix his ear drums that would burst being so close to such a shock wave, that or he has constant tinnitus, and has to learn sign language, for communication, both make sense and I haven't decided yet, maybe Ill have both, where he goes deaf for long periods of time as his body heals from the after affects of his explosions, so he learns sign language because it makes sense to do so.
he has enhanced joint strength, allowing him to not dislocate his shoulders or hips every time he uses his explosions, along with his fingers not bending 180 degrees backwards, and you know him not breaking his neck or compressing his spine every time he flies.
he dyes his hair black or gets it permanently changed by a quirk barber, since explosions cause, you know soot, black soot, which I'm sure stains the shit out of his hair.
He has glasses since being that close to bright ass explosions probably do a shitload of damage to your eyes, of course, the healing factor heals this too after a period of time, but he has them till then. they also would have interchangeable lenses since the damage would be different every time(this likely wont matter in the story I just enjoy these little details).
right now with his physical characteristics done lets go into his situation and emotional and mental characteristics, he is of course still going to be and incredibly angry person, and immensely prideful, it just wouldn't be Bakugou otherwise, but I think his pride would cause him to make rash decisions, like thinking he could survive on his own, and taking a bet from his mom (not serious on her end) that he couldn't last a day on his own without her and his dad, so running away from home, and getting a taste from the real world, living on the streets for a while, finding a job (ironically at a library) where he self studies ahead of his grade level because Bakugou is like referred to as a genius multiple times, so realistically he is likely quite gifted, and probably could have skipped grades in middle school (same for Izuku really), he unfortunately can't afford any martial arts training because poor, and barely affording an apartment, but because he now has to live in a shady neighborhood his pride, temper, and shit social skills, will get him into a lot of fights, so he has plenty of practical brawling experience for someone his age(which he wouldn't have if he stayed in school because beating the shit out of skinny twerps and middle schoolers doesn't make you better at fighting).
story wise we also have a lot of potential, such as his parents and the police looking for him, along with Izuku, who of course finds him, because I have to have a reason for Bakugou to actually have a reason to dislike him, because seriously a guy with so much pride really shouldn't give a damn about what Izuku thinks and shit, I need a rivalry between the two since he along with Todoroki are the only people who can match Izuku, well not in the manga sure, but Katsuki has the agility of a rocket with the power output of a MOAB, and even more when he is fully grown and trained, and Todoroki is literally walking around with more potential energy output than a nuclear reactor with the possibility to even expand on that with pretty much unlimited amounts of ice/water and fire/heat at his disposal, he is like a walking gold mine of middle fingers to thermodynamics, and perhaps with the output of a small nuclear bomb when using his super moves of course with none of the radiation, I don't care how big your muscles are and how cool your black ropes and personal anti-gravity and smokescreen is, you are not better than the US governments wet dream, and a walking fuck you to science and god.
Alternatively, I'll be making other changes to quirks and characters.
Ochaco Uraraka/Uravity, her quirks name is Gravity, and she seems to be able to simply remove gravity from someone but this indicates she should be able to add gravity, which I will be giving her the ability to do, also there might be the chance of her being able to decide which way gravity effects people instead of her nullifying it, since having gravity going up while pulling down equals zero gravity.
Mezo Shoji/Tentacole, also seemingly underutilizes his powers, such as having regeneration and the ability to reabsorb limbs, having enhanced strength for his arms, and having enhanced senses, also he should feasibly be able to instead of adding arms add muscle to his arms.
Tsuyu Asiu/Froppy, doesn't have the strength her quirk should give her, also she would be a much faster runner than a hopper, she also doesn't seem to have any interest in martial arts despite her quirk making her incredibly suited for it, she also should have incredible night vision, the ability to breathe without lungs or a mouth/absorb some oxygen through her skin, secrete a multitude of incredibly paralyzing and numbing poisons, the ability to survive for years without water if she needs, and have an insane amount of flexibility.
Mishrao Ojiro/Tail Man, his tail is incredibly muscled and strong, likely with bones in it, he should be using it for most if not all of his attacks it should be able to lift at least 3-4 times his weight, also with it being prehensile, he should be using it for grappling which means he should be practicing Brazilian ju-jitsu or another grappling based martial arts.
Denki Kaminari/Chargebolt, his power is the most underutilized out of the entirety of class 1-A or even the entirety of the first-year hero course, he could be channeling electricity through his nerves for quicker reaction time and body movements(aka he could be faster than everyone in the class except Deku and Iida), or through his hands to tase and stun people, hell he could be channeling it through his torso to each arm and creating an arch of electricity that he can snap out like a whip(it would be very unpredictable but its something) he should be a melee fighter either way, with grappling as his fighting style, since you know he is a walking Tazer/lightning bolt.
Eijiro Kirishima/Red Riot, he literally increases his density and turns his body into a rocklike substance, which means a couple of things, he can exert more strength, its hard to tear muscles when it takes the same amount of pull to tear them as it does rock, not only that, he definitively has a large increase to his physical strength, the world must feel like cardboard to him when he is fully hardened, also he can seemingly through training increase his hardness and density, allowing him to become even stronger due to the need to be able to continue to move while hardened, also he can seemingly decide the flexibility of his hardness since he is able to move while in his hardened state, also he has built-in brass knuckles, he should focus on boxing since due to his weight, falling over is a far larger problem than for a normal fighter, also his entire body gets sharp, meaning anyone who strikes him hurts themselves, making him one of if not the best melee fighters in 1A.
Koji Koda/Anima his power is very mysterious, also it brings to question the sentience of creatures other than humans, if they are sentient he is forcing them to do what he wants, also seeing as how he can do that he should be able to force people to do what he says since we are just highly intelligent animals if they aren't sentient he gives them sentience either with an instilled loyalty to him or he then forces them to listen to him, which means he should be able to force anything into sentience, or at the very least be able to do so to plant matter, he also seemingly has rocklike skin, and is quite physically large meaning he would be a good melee fighter with his animals as support.
Rikido Sato/Sugarman, His quirk is pretty straightforward, but he should be able to power up a lot more with liquidated and compressed sugar, allowing him to feasibly strengthen up enough to be near equal to allmight for a short period of time, also he is incredibly large and muscled for his age, he should be able to handle many threats without his sugar, also he could go all bane and have a constant influx of sugar into his system, along with that he shouldn't become stupid with his powerup since sugar doesn't do that, also he shouldn't become stupid at all, incredibly lethargic yes, but he could technically fight through that with will, although the strain on his system might screw over his health, or his quirk might take care of that, allowing him to process sugar in a way that no matter how much he eats it doesn't affect his health.
Kyoka Jiro/Earphone Jack, there is not much I can do with her quirk, however being able to change the loudness, and pitch of the noise should do something for her, also her jacks seemingly are strong enough to be helpful in melee combat, yeah she should also learn a martial art just because she is quite lacking in that.
Hanta Sero/Cellophane, his tape doesn't seemingly have any stable properties, telling me he can improve the strength, stickiness, and control over his tape, allowing him to be very similar to spider-man, actually, that is one of the main facets of his quirk that I think is underutilized his ability to seemingly web swing, allowing him incredibly amounts of mobility, his elbows also seemingly are quite large and dense, which could afford him some good striking power, he also could use elbow strikes to stick his tape, allowing for a unique fighting style.
Mina Ashido/Pinky seemingly can change the characteristics of her acid, as such I don't know why she couldn't make it incredibly sticky, of course she already makes it very slick as well, but as a hero, where capture is the most important facility of Villian takedowns, It would make her incredibly useful, and likely one of the best in the class when it comes to being a pure hero.
Toru Hakagure/Invisible Girl, her power is passive however she seemingly can with enough focus cause a fractal effect, which leads me to believe she could eventually when exposed to bright enough light give herself a laser effect, this, of course, would be an incredible boon for fighting, also she may be able to do a flashbang effect, of course, she also would be an incredible melee combatant, so long as she focuses on striking and not grappling, as she is quite small and not very strong.
Minoru Mineta/Grape Juice, actually, and unfortunately does have some potential, he seemingly bounces faster and faster on his balls, so in theory, he could use that to speed up to a mean punch, also he could be one of the fastest in the class if he used his spheres as a mode of transportation instead of just capture. (I still might just replace him with shinso anyway)
Hitoshi Shinso/Mastermind, Quirk is incredibly overpowered when used right, what's stopping him from using it on himself to go past physical limiters the body puts on itself, or go through grueling training sessions without being tempted to quit, he also despite needing an answer should be able to circumvent that through various means such as seeing physical movement as an answer or using sign language, many different things, either way, he could be a devastating physical combatant or a trickster, plus he catches the eye of Aizawa who clearly gives him special training due to him, really needing it, the boy while tall is not physically imposing whatsoever, he has incredible potential beating out much of the class, especially since his power could likely beat allmight given the right circumstances.