As you cross the border, the immigration office is in the blue SAT Aduanas building on the right.

Yes. Parking is available in two areas. (1) The easiest way - follow the Declaration Lane signs into a parking area. This parking area is closest to Mexican Immigration (INM). AFter visting Immigration, it's easy to leave the parking facility to cross the border. Or (2) after crossing the border, just past the overhang as you leave the facility, there are spaces in the center toward the back. You may have to do a left or right u-turn in order to park. Look for the blue and yellow signs on the chain link fence that read Area de Inspección/Inspection Area. The parking lot is right after the chain link fence. Ask a customs official where you may park if you have any doubts.