In some fanfiction, Snape's portrait has the ability to possess or influence the living. This could be used for good, like helping a character perform a difficult spell, or for more devious reasons if the plot calls for it. It adds an interesting dynamic to the story as the living characters have to deal with this unexpected influence from the portrait.
The portrait could be more open and less guarded. While the real Snape was often secretive and brooding, the portrait could be more forthcoming with his feelings. For example, he might openly express his pride in the students he once taught, especially those who have gone on to do great things in the wizarding world.
The interaction could be really interesting. Snape is a complex and often brooding character. The Teletubbies, on the other hand, are all about joy and simplicity. Snape might try to analyze them as he would a magical creature. He might be frustrated by their lack of understanding of his world. However, the Teletubbies' positive attitude could start to affect Snape. They could show him that there's more to life than just the dark arts and his grudges. For example, they might get him to play in their meadow, which would be a completely new experience for him.
It could make him more confident. Just the fact that he has a connection with Snape through the portrait might boost his self - esteem.
In many fanfictions, Snape is often the more reluctant one in the relationship. His love for Lily still lingers in his heart, but Bellatrix's allure and power draw him in. For example, in some stories, Bellatrix uses her seductive charm to break through Snape's cold exterior.
Snape would probably start off being rather aloof. He'd observe the Avengers' behavior and abilities before making any real moves to interact. He could be sarcastic towards them, especially if they make assumptions about him or his magic. But as time goes on, he might start to see their value and open up a bit more, sharing some of his magical knowledge.
In some fanfiction, Voldemort and Snape interact in a very master - servant kind of way. Voldemort gives orders and Snape follows, but with a hidden agenda. For example, Snape might be subtly changing the Dark Lord's plans without him noticing.
Often, they start off as adversaries. For example, in many fanfictions, Snape's dark and brooding nature clashes with McGonagall's no - nonsense attitude. But as the story progresses, they might find common ground in protecting the students or in the face of a greater threat to Hogwarts.
In a 'living with dragon' fanfiction, Neville could find a way to use his knowledge of plants to feed the dragon. He might discover certain magical plants that are a dragon's favorite. Ginny would be fearless and would probably be the first to try and train the dragon to do tricks. The Weasley twins would surely come up with some inventions to make living with the dragon more fun or easier. The dragon would also interact with the Hogwarts ghosts. Peeves might play tricks on the dragon, while the Fat Friar would try to keep the peace between them.
Snape would likely be disdainful towards the Dursleys. He has little patience for Muggles in general, and the Dursleys' mean - spiritedness would not endear them to him. He might use his cold, sarcastic tone on them, leaving them confused and a bit frightened.
One interesting story could be about Snape's portrait giving secret advice to a young wizard. It might use his past experiences to guide the youngster through the challenges at Hogwarts.