In many such fanfictions, there could be a lot of different scenarios. One possibility is that the wizarding world would be in chaos. Dumbledore might lead a frantic search for baby Harry. Maybe some of the Order of the Phoenix members would try to infiltrate Voldemort's lair to rescue him. It could also be that Voldemort has some strange plan for Harry, like trying to turn him to the dark side from a very young age.
Harry could also try to reason with Voldemort. He might remind Voldemort of the prophecies and how killing him might not be in Voldemort's best interest. He could also try to appeal to any bit of humanity that might still be left in Voldemort, although that's a long shot.
A third plot twist could involve a character we least expect coming to Harry's rescue. Perhaps a Slytherin student who has been secretly against Voldemort all along. This student could have some inside knowledge about Voldemort's lair and manages to free Harry, leading to a change in the dynamic between the houses at Hogwarts.
Yes, there are likely some fanfictions out there with such a wild concept. Fanfiction often explores very strange and unique ideas, and this is definitely one of the more out - there concepts. However, it's not a part of the original 'Harry Potter' canon.
In a fanfic where Voldemort kidnaps Harry, it could lead to a lot of intense situations. Harry might be used as a bait to lure his friends into a trap. Or Voldemort could try to turn Harry to the dark side, using various forms of dark magic and psychological manipulation.
Well, Harry might discover some hidden passageways in Voldemort's lair. Since he has a lot of experience with tricky situations at Hogwarts, he could use his wits to find a way out. Also, he could try to appeal to any shred of humanity left in Voldemort's followers, if there are any, and get them to help him escape.
In some fanfictions, Hermione might use her wits to try and outsmart Voldemort. For example, she could pretend to be on his side while secretly planning an escape or a way to undermine his plans. She's very intelligent, so she could try to find a weakness in Voldemort's defenses or his followers.
It would be very strange. It might involve a lot of magic to make such a situation possible in the first place. Maybe there would be a powerful dark spell that forces this situation. And then it would deal with how Harry copes with having a baby that is related to his greatest enemy.
One common theme is the struggle between good and evil within the child. Since the parents are on opposite sides of the moral spectrum, the baby is likely to have an internal battle. Another theme is acceptance. How the wizarding world accepts or rejects this strange union and the child. And also, the theme of power, as the child might inherit powerful magic from both parents.
One possible reason could be that Voldemort sees Harry as a symbol of innocence that he wants to corrupt. Just like how he enjoys toying with his enemies, treating Harry like a baby might be a way to belittle him and make him more vulnerable in his eyes.