I think Ultimate Deadpool is a mutant, they even hinted to this saying that he survived "death-defying" battles in the Wakandan war. And after Shadowcat made him explode, he's shown being intact (albeit shadowed).
How did Ultimate Deadpool become a cyborg if he heals rapidly?
Well, I think his healing is like a river. If you abstruct the stream, the water will flow around the obstruction.
His healing factor isn't going to heal cybernetics. So after he blew up, his body was free to heal correctly.
Well then why would a group of mutant-haters be so loyal to a mutant?
I think they explained their philosophy. It's not that they hate mutants, they just think that it isn't right that any punk can have powers, and that they should earn those powers.
Deadpool's their commanding officer, saying that they've fought in wars together. So to them, Deadpool "earned" his powers.
I'm thinking X-Men and Spider-Man may have proved to Deadpool that they earned their powers, so any future interactions between them may be very different.