Definitely not. Spiderman has always been a part of the Marvel Comics universe. Marvel has its own distinct set of characters and storylines, and Spiderman is one of the most famous among them.
Spiderman is Marvel, no doubt about it. He's got that classic Marvel charm and his storylines are deeply integrated into the larger Marvel comic universe.
Well, it could be really interesting. Spiderman's acrobatic fighting style and his quippy personality would be a fresh addition to the DC universe in fanfiction. He might team up with Batman, and their contrasting detective and street - level hero skills could make for some great adventures. Maybe he'd also have some run - ins with the Flash, comparing their super - speed in different ways.
There are quite a few out there. Some might focus on how Spider - Man interacts with different DC characters in a harem - like setting. For example, he could be in a world where he meets various female DC characters and forms unique relationships with them. You might find some really creative stories if you dig deep enough into the fanfiction community.