A prince of time destroys time. Does that mean he could stop time loops and certain paradoxes?

Likely not, severing a Time Loop and allowing it to be left unfinished seems like a handy power, but by the integrity of Paradox Space’s Timeline system, that just. Wouldn’t work. If you stop a Time Loop half-way, you’re preventing it from starting it, which means whatever already happened wouldn’t have happened. Unless by ‘stop time loops’ you meant they sort of. Insert themselves there and complete the Time Loop in a different way than it was intended but still effectively close up everything, then by all means, that could be an interesting take.