Does feeling the urge to enter the restroom, or feeling bubbles exit during prayer, invalidate the prayer or nullify ablution, especially given severe obsessive-compulsive tendencies?

You must fight off whisperings (waswas) and ignore them, and not pay them any attention. If Satan whispers to you that you need to use the restroom, continue with your prayer and do not interrupt it. And if he whispers to you that something has come out of you, act with certainty of purity and do not assume that anything has exited.