Is there a difference between the signs for 'potty', 'bathroom', and 'toilet'?
In everyday ASL, the shaking 'T' handshape is commonly used interchangeably for 'potty', 'bathroom', 'restroom', and 'toilet'. Context and the age of the person you are speaking to will usually clarify the exact English translation.
How hard should I shake my hand?
A gentle, relaxed shake from the wrist is perfect for normal situations. However, if it is an absolute emergency, signers will often shake the 'T' handshape faster and more vigorously while showing urgency on their face!
Do I use my right or left hand?
You should use your dominant hand. If you are right-handed, use your right hand to form the 'T' and shake it. If you are left-handed, use your left hand. Either way is perfectly correct.