About the Immigration Office: (INM - Instituto Nacional de Migración)
As you cross the border, the immigration office is in the blue SAT Aduanas building on the right. The entrance to the office is on the outside of the building up a few stairs.
Yes. Parking is available in two areas. (1) By following the Declaration Lane 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.
Note: This article only describes the small immigration office where Mexican tourist cards are issued. For resident cards and visas, visit the main immigration office.