The two months of calmness were only possible due to the fact that harry had completely ignored the trouble on Halloween, plus the addition of hermione having no reason to be upset due to other students constantly complaining about her haughty attitude in the class or lack of social skills. Hermione had more than ingrained into the class with harry's constant reminders from even before coming to Hogwarts.
Ron and other hot headed boys of the class did get into several petty fights with the slytherin's but Harry had made sure to keep himself away from any interference and also advised Hermione that these should be solved by the students among themselves as Hogwarts did not have any rules against petty skirmishes, only intent to severely injure or harm a student will be taken seriously, especially when it came to Slytherin and thus it would be no use even if they had informed, other than getting unnecessary ire from the students involved.
Neville was the only one that Harry had taken the initiative to make friends with in the class. Harry knew that the first few years of Hogwarts were unbelievably tough for the young Longbottom. In the previous time harry at least had made friends when he came to Hogwarts but due to his silly and under confident nature Neville had no strong bonds of friendship till at least the fourth year. Neville also had a big issue that held him up till his fourth year, his wand.
Neville was the heir to a most ancient and noble house and he only had his grandmother left after his parents were tortured to insanity by Bellatrix Lestrange. Unlike Harry who knew nothing of his family or parents, Neville had grown up hearing stories about the strong and valiant Frank and Alice Longbottom from his grandmother. Harry knew one thing that even Neville did not, when the prophecy was made there were two candidates, the Potter's and the Longbottom's.
It was true that both the couples were exceptionally gifted and strong on the battlefield and had even gained the upper hand thrice against voldi's major forces but it still came down to Voldi's personal decision to select the child of Potter's as the potential fulfiller of the prophecy. Snape had heard half the prophecy before he ran away and it was then discussed in the private gathering of Voldi's most trusted followers so that they could select how to destroy the threat.
It was always true that they had never planned to leave either of the child alive, it was just the matter of which would have Voldi's personal attention. In the discussion most were in the support of the Longbottom's child being the child of prophecy because this was a most ancient and noble house, coupled with the fact that the child would be a pureblood made them think that the Potter child would not be as much of a threat considering he was to be a halfblood, but unexpectedly Voldi had chosen to personally destroy the Potter's rather than the pureblood because only Voldi knew that he himself was a halfblood.
One could call Neville both lucky and unlucky in surviving the catastrophe, even though he was safe, he was now left to be raised in a household that had a grieving, strong willed, hot headed, mother as the head, who after the loss of her son had refused to accept reality and placed so much burden on her young grandson that he was unable to ever feel free in his own house. His grandmother had started comparing a young boy of four to a full fledged auror who had the qualifications to stand and fight one of the cruelest dark lords seen.
Harry had no understanding of the wizarding world when he first arrived, which was the reason why he never had any shackles of thoughts but Neville had been constantly reminded since his childhood about the greatness of his parents and it was not simply to the point of understanding but rather to the point of fear in his very being, that he was to be as excellent as his Father since the beginning. This lead to the collapse of the young child's confidence in himself almost to the point where he couldn't awaken his magic days before the Hogwarts acceptance letters were to be sent out.
Even after he was selected to attend, his grandmother had not let go of her foolishness to preserve her son's memory, by not allowing Neville a wand of his own but rather forcing his Father's wand into his hand. Harry had no plans to go against the natural order as Neville himself will break his wand during the third year and from then on everything will proceed comparatively smoothly. It was not that Harry did not wish to help but he could not interfere in the household matter of another prominent household without revealing his own status.
Harry made sure that he was partnered with Neville for most of the classes so as to prevent him from committing minor mistakes due to his nervousness and to remind him that he still got a chance to do good and make friends. These small nudges had greatly helped Neville in slowly settling down in the school, Though he was still clumsy and had not managed to make strong bonds of friendship he was at least able to speak with everyone in the house without major hesitation.
Harry also nudged him towards the one subject that Neville will later show great success in, Herbology. He had shown Neville several books on Herbology that were rather well hidden in the library. As was expected Neville had taken great interest in Herbology and was now less bothered about loneliness due to lack of friends.
Apart from this Harry had also informed Daphne about the new schedule that he had informed Hermione about, so that she would not make extra plans and also advised her to do the same for the rest of the term. Harry was not concerned about the stone or Voldi because he was well aware that with his current prowess he should not entangle himself with either of the two great dark wizards plans and play into their hands.
Harry had approximately six more months before the first year ends and he was set on completing one additional subject upto basic mastery before the next year and so he and Hermione had discussed and because they would now be spending most of their time in the common room they chose a subject that could be more focused on theory and understanding of magic rather than flashy wandwork, Runes.