Would Sonic 1, 2, 3&K, and CD from Sonic Origins be allowed in the Sonic 8? Or do the added features such as the drop dash and spin dashing in Sonic 1 invalidate it?

I would say there's no reason for them to invalidate it so go for it. They are different versions of the same game and have different glitches and tricks so the OG will still be faster with the glitches but if you're doing NMG then there should be little difference.

Hopefully a mod can confirm they're allowed but I don't see why they wouldn't be.