This is a very strange and inappropriate concept for the Naruto series. The Naruto series is mainly about ninja battles, friendship, and the pursuit of dreams. Such a fanfiction goes against the positive themes of the original work, so it's not something that should be promoted.
Well, if Naruto is captured by Orochimaru in fanfiction, one possibility is that Orochimaru wants to use Naruto as a bargaining chip against Konoha. He may think that by having Naruto in his grasp, he can force the Hidden Leaf to meet his demands, like giving him access to certain forbidden jutsu or secret scrolls. Another aspect could be Orochimaru's curiosity about Naruto's ability to master new jutsu so quickly. He might want to study Naruto's mind and body to find out the secret behind his growth as a ninja.
Yes, there are likely some 'Naruto Gets Pregnant' fanfictions out there in the vast world of fan - created content. However, such concepts often deviate from the original source material in very extreme ways.
Naruto would be angry. He's not the type to just accept being kidnapped. He'd immediately start looking for ways to escape. He might try to use his ninja skills to break free from whatever restraints Orochimaru has put on him.
Naruto getting kidnapped by Orochimaru would be a really dangerous situation. Orochimaru could start by putting Naruto in some sort of chakra - suppressing device. This would limit Naruto's ability to use his Nine - Tails power. Then, he might try to implant some of his cursed seals on Naruto, which would give him more control over Naruto. But Naruto has his own allies within himself. The Nine - Tails, despite their rocky relationship, might help Naruto out in this situation. Also, Naruto has the memories of all the people who care about him. He'd draw strength from those memories and keep his hope alive, waiting for the moment when he can break free and return to his friends and the village.
I'm not sure if there is such a specific fanfiction. Fanfiction can cover a wide range of very creative and sometimes out - of - the - ordinary ideas, but this one seems rather unusual. You might try searching on some large fanfiction websites to see if it exists.
I'm not sure if there is a single 'popular' one in the sense that it's widely known. Fanfiction is a vast world with so many different stories. Some people might write this type of fanfiction for the shock value or to explore a different relationship dynamic. But it's likely that most Naruto fans are more focused on the canon pairings or more established fan - created pairings. So it might be a bit of a niche within the Naruto fanfiction community.
There might be such a fanfiction. However, it's important to note that a lot of fanfiction is unregulated, and the quality can vary greatly. If it does exist, it could be on large fanfiction platforms like FanFiction.net or Archive of Our Own. But you would have to use their search functions and look for it specifically.
I'm not sure if there is such a specific fanfiction. Fanfiction topics can be extremely diverse, but this one seems rather unusual and might not be common. It could also potentially violate the spirit of the original Naruto story which focuses more on their friendship and rivalry rather than this kind of relationship.
In fanfiction, almost anything can be possible as it's a realm of creative interpretation. However, this concept goes against the original nature of the Naruto series where Naruto is male. But in fanfiction, some authors might use magic or some unique plot devices to make such a situation happen, but it's not in line with the canon.