Welcome to the forum. First might I suggest that the forum is divided into forums for each state. Your questions will be answered more quickly and with greater accuracy if you post California specific questions there.
As for "carrying while tattooed", as far as I know this is not a crime in any of the fifty states. But you are correct in assuming that the combination of a sidearm and a lot of tats might draw unwanted attention. I am not really the best person to ask about this because I do not have any tattoos, but others will be along soon to respond in that area. My thought would be that you might try long sleeve shirts to offset your concerns while carrying.