If you paid for your tags and then later got your car smog. Can you go and pick up your tags at DMV ?

Yes you can. Don't take longer than 1-2 weeks cause then they'll mail them to you.

Depends how you paid. If you paid online, mailed in your payment, or paid at the kiosk, then the tags will be mailed to you. If you paid in the office at a window, then you have to go back to pick it up.

Yes, within a week