What problems to expect if battery disconnected

You probably will lose radio settings and the engine may have to relearn your driving habits all over again, even the power windows may not work properly. If everything works then no worries but next time use a code scanner to reset the engine lights. The gas cap light still being on may mean you need a new gas cap or at least a new gasket on the cap.

Again, FOR's probably correct. Before disconnecting the neg battery terminal (don't bother with both), you might try restarting a 4th time after the gas cap CEL, as it might self-clear once the cap is tight. If not, THEN disconnect neg terminal overnight, remembering that the first restart will take a few seconds as the system reboots. Subsequent restarts should be instant. Easy peasy.

The guys at a repair shop replaced my passenger side low beam headlight bulb and now the cruise control doesn't work & it's light flashes, the brake light is on, the check engine light is on, and the traction control light is on. I know they said they disconnected "something" on the engine to replace the right side low beam bulb rather than go up through the fender from below. I will try disconnecting the battery to see if they will reset. If that doesn't work, the shop says bring it back in.