Waste of money. If you take it most anywhere, you will spend a LOT of money for them to GUESS.
SO.......
Just slow down. Wait till you get the new alternator on. If the BAS/ESP light wont go out, replace the battery.

THEN and ONLY THEN should you start throwing money at the BAS/ESP light. You have an electrical disturbance in the car, the alternator was undercharging - dont go all half-cocked after a problem until you resolve the FUNDAMENTAL issue.