One common theme is the clash of two different worlds. Harry comes from a world of magic and Jon from a more medieval, political world. Another could be friendship, as they both are heroic characters. They might bond over their shared sense of justice.
Yes, there are quite a few. Some explore alternate universes where Harry somehow exists in the world of Jon Snow. You can find them on various fanfiction websites. Just search for the specific tags related to both characters.
Jon Snow could potentially have allies like the Mormonts. They have always been loyal to the Starks. Maybe even some of the Dornish houses might side with him. They have their own reasons to oppose the current power structure in Westeros. And of course, his friends from the Night's Watch who left with him or believe in his cause could be his allies in this conquest. He might also gain the support of some of the maesters who see the value in his leadership for the future of Westeros.
One main theme is the clash of different worlds. Harry Potter's magical world and Jon Snow's more medieval, political world are very different. When they meet in fanfiction, it often explores how these differences create both conflict and cooperation.
It could be really strange. Maybe Jon Snow would be revealed to have some hidden connection to the Potter family, like a long - lost relative. He might bring his 'Game of Thrones' - style fighting skills and sense of honor to Hogwarts.
One possibility could be that he would bring his magical skills into the world of Westeros. He might use magic secretly to gain an edge in battles, like creating distractions or protecting himself and his allies. For example, he could use a shielding charm during a skirmish with the wildlings.
Daenerys Targaryen could be one to help. Since she has experience with dragons, she could give Jon Snow advice on how to care for the egg and hatch it.
It could be a young and untainted Frey. Maybe a niece or a cousin of the more infamous Freys. One who has not been involved in the past atrocities committed by her family and has a more noble heart.
Daenerys Targaryen is often paired with Jon Snow in such fanfictions. Their combined power and the potential for a different kind of relationship makes it a popular choice among writers. Another character is Arya Stark. Their sibling bond can be explored in new ways when Jon is reincarnated, like Arya helping Jon with her assassin skills in a different plot line.
The North would surely support him. They have always seen him as one of their own and a great leader. Also, the wildlings might back him, considering he has a history of working with them and understanding their plight. Davos Seaworth would most likely be on his side as well, given his loyalty to Jon in the past.