Are any nightcore songs legal on this site?

No, this is clearly wrong. You don't have to make an exact copy of a work to violate its copyright. People get sued because a six bar snatch of their new song has the same melody as a six bar snatch of the other song. Rap recordings that sample a tiny, tiny segment of an earlier recording have to get permission and pay royalties.

I'm not sure what "legal on this site" means in the original question. Does it mean legal as in following the law, or does it mean permitted by us?

I am not a lawyer and the following is not legal advice. We believe that you can legally use copyrighted material all you want in a private project. But in a shared or published project, you need permission to use copyrighted material legally.

As for our policy, we (following Scratch on this) do not examine your projects to enforce copyright law proactively. The law does not require us to do that. But if we get an official DMCA takedown notice from a copyright owner, we are legally required to unpublish and unshare the project about which we get the complaint. As a practical matter, it's very unlikely that a copyright owner will consider it worthwhile to police Snap! projects, although I can imagine that some project goes viral on Twitter and then they send us a takedown notice.