Yes, there are quite a few out there. You can start by looking on popular fanfiction websites like Archive of Our Own. Just search for 'Peter Parker cuddles Natasha' and you'll find various stories with different plotlines and interpretations of their relationship.
Well, AO3 is probably the top choice. It allows for detailed tagging, so you can narrow down your search precisely to stories that involve Peter Parker and Natasha cuddling. Another place could be Tumblr. There are often fanfic recs (recommendations) on Tumblr blogs dedicated to Marvel fanfiction. You might have to do a bit of digging through different blogs, but it can be a good source. Additionally, some smaller, more specialized Marvel fanfiction communities might also have stories like this.
Thor would be a likely candidate. Since he is Loki's brother, he already has a connection with him. Thor might be the one to convince the other Avengers to give Loki a chance and be the first to reach out and try to befriend him in this new situation.
One aspect of Loki and Peter's friendship in fanfiction could be their shared experiences of being outsiders in some ways. Peter, as a young superhero, might not always be fully understood by the adults around him. Loki, having his own issues with his family and the Asgardian society, can relate to that feeling. Their friendship could develop as they confide in each other about their insecurities. For example, Loki could share his tales of trying to prove himself to Odin, and Peter could talk about his struggles to balance his normal life with his superhero duties. This mutual understanding could strengthen their bond.
Future Loki might interact with the Avengers in a cautious way. He knows their past opinions of him and tries to prove himself. He could start by sharing small bits of useful information. For example, he might tell Iron Man about a weakness in a new enemy's technology.
In this fanfiction, Loki might interact most with Hulk. It would be an interesting dynamic as Loki is a master of manipulation and Hulk is, well, the Hulk. Loki could either try to use Hulk for his own purposes, which would be very dangerous, or he could end up on the wrong side of Hulk's anger. But at the same time, it could also lead to some unexpected moments of understanding or at least a begrudging respect between them.
He would probably interact a lot with Thor. Since they are brothers, there is a pre - existing relationship full of complexity. Also, he might interact with Iron Man quite often. Tony Stark's sarcastic nature and Loki's trickery could lead to some really interesting exchanges, either in the form of verbal sparring or working together on some high - tech and magic - combined projects.
Well, Thor might be a bit shocked at first. He'd probably be amused by some of the wilder interpretations of his brother in the fanfiction. Captain America, on the other hand, would likely be confused by the whole concept as it's so different from the traditional stories he's used to. Iron Man would probably make sarcastic comments about how creative the fans are in coming up with these stories.
In these fanfictions, one characteristic is the use of Loki's shape - shifting abilities for comical purposes. He could transform into different Avengers and act in a way that is completely out of character for that person, causing confusion and laughter. Also, the stories often play with the power dynamics among the Avengers and Loki. Loki might try to outwit them in a humorous way, like in a game or a competition. The humor also comes from how the Avengers, who are used to serious threats, deal with Loki's more light - hearted and silly challenges.