Is it bad to clean your belly button piercing with rubbing alcohol?

Yes, it's bad -- that's way too harsh for your piercing. Try doing sea salt soaks. Dissolve 1/4 teaspoon of non-iodized sea salt into 1 cup of very warm water. Soak your piercing in this solution for about five minutes. You can pour it into a shot glass and then press the glass over your navel to create a seal.

Antibacterial soap can even be too strong for some. If you want to try a soap, I recommend Satin -- it's an antimicrobial soap that is gentle enough for new piercings. Your piercing shop ought to stock it, and you can also find it online.

Yes. It will irritate the piercing. I recommend you melting sea salt into warm water in a shot glass (or small glass) and placing it on your navel. That will prevent infections.

Uh...yes. That's way to strong. All you need is anti-bacterial soap and water.