Peter might get a bit flustered at first. He's young and looks up to the Avengers, so being made fun of could make him blush or stammer. But then he usually bounces back with a witty comeback of his own. For example, he might say something like 'Well, at least I don't have an old - fashioned shield' to Steve if Steve teases him about his suit.
Well, sometimes in fanfic the Avengers make fun of Peter's suit. They could say it looks like a pajama or something. Maybe Tony Stark, in a teasing way, comments on how Peter's web - shooters are a bit too 'homemade' compared to his high - tech Iron Man suits. Another instance could be that the Avengers mock Peter for his clumsy moments when he first joins them, like tripping over his own feet while trying to show off his acrobatic skills.
Tony Stark might use his quick wit and technology. He could immediately scan Peter to make sure there's no physical danger causing the hyperventilation. Then he'd probably crack a joke to try and calm Peter down, like 'Kid, you breathe any faster and you'll fly away like a human jetpack.'
Peter is likely to be in awe. He might be a bit nervous at first, but also extremely excited. He has looked up to the Avengers for a long time, so meeting them would be like a dream come true. He would probably be stuttering a bit as he tries to introduce himself and show his respect.
One way is by getting involved in Peter's school life in a more official capacity. Maybe they could arrange for some anti - bullying seminars at the school. Natasha could also train Peter in stealth and evasion techniques so that he can avoid the bullies more easily. Thor could even offer to be Peter's bodyguard for a while, at least until the bullying situation is resolved.
The Avengers would initially be in shock when they find out Peter is sick. Clint Barton would be the one to keep a calm head and start organizing things. Wanda Maximoff would try to use her powers to ease Peter's pain if possible. Vision would use his vast knowledge to try and find a solution. They would all be very concerned and do everything they can to make Peter better, from getting the best medical help to providing a safe and comfortable environment for him to recover.
The Avengers might react in different ways. Steve Rogers would probably be polite but firm in getting to know Peter's boyfriend. He'd want to ensure that he was a good influence on Peter. Thor, on the other hand, might be a bit more boisterous. He could either be really friendly and enthusiastic, or his loud and powerful presence might accidentally scare the boyfriend a bit.
Well, in this fanfiction, Peter Parker might meet the Avengers in a more casual setting. For example, he could be at a science expo where some of the Avengers are also present. Peter is there to show off his latest web - shooter design. The Avengers notice his intelligence and his unique abilities as Spider - Man. They then start a conversation with him, and from there, a relationship between Peter and the Avengers begins to form. This could lead to Peter getting involved in more Avengers - level missions and growing as a hero.
Well, in many fanfictions, the Avengers protect Peter by always having his back in battles. For example, Captain America might shield him from incoming attacks with his iconic shield. They also offer him guidance. Tony Stark could be constantly giving him advice on how to improve his suit and combat skills.
Peter could rely on his own inner strength. He has a strong moral compass, so he might use that to remind himself that the Avengers' actions are wrong, not his. And then he could focus on using his Spider - Man skills to prove his innocence or protect himself.