No. I have spiderbites and they didnt numb it either time, nor have any of my friends had theirs numbed. Besides the piercing itself doesn't hurt. You'll feel a prick. The after math of the piercing...
No, most piercing places do not have anesthetics on hand. If you talk to your doctor ahead of time, they might be able to set something up with you though.
Numb or not it is never safe to perform your own piercings at home or anywhere else and this site will not provide information that can lead to personal injury due to errors or your own stupidity....