New radio, door lock’s malfunction?

The door locks and other retained memory items (linked to the key or fob that adjust when a different one is used) store that memory in the original radio. Remove the OE unit and you get issues with things that use that memory or linking feature. The common thing to do is to remove the OE unit and install it someplace like the glove box or under a seat with the speaker outputs disconnected. Then you don't lose any of the functions that the OE unit controlled.

Is there a way to add or reprogram info with new head or the fob, or? Also, I got it installed at Best Buy and the installer insisted the door lock issue had nothing to do with the installation. I am frustrated and considering taking out the new and reinstalling the old.

Probably not able to do anything with the new unit as it doesn't have the correct network abilities. Not saying that it applies to all "installers" but at the local BBs the folks doing installs were flipping burgers a week ago. I've seen them install a car starter and a couple weeks later the car won't start with it or the key. Tear into it and discover they just twisted wires together and taped them, or used vampire taps that cut the wire because of the design. If you have access to a factory scan tool you could use it to test out the system and see if it was the loss of the radio or if the install cut or damaged other wiring.