I've known fuel pumps to do that on occasion. The first step would be to check fuel pressure; it should be 50 psi at idle and go up to 58 psi under acceleration. Residual pressure should be 36 psi after 10 minutes. If the fuel pump is faulty, be sure to replace the filter as well.
Before I give you a bonus, you received an excellent from me already as I took the car out for a "drive", it all points to the fuel system, and as I tested it for how long it ran crappy before it cleared up, you can tell it was pressure. Good call, I hope! one hat did they do? One other thing I got the car used , they put in an Alpine, picked stations up fine. Had AC replaced and I get nothing now. I checked and antenna is connected. Antenna amp have a fuse or shorted out? What did they do?
The antenna amplifier is powered by the head unit through the big antenna wire. They are known to go bad. Here is a graphic depicting its location in the driver's side 'D' pillar: