While driving, all warning lights on dash suddenly were lit. When I stopped the car, it wouldn't start again and sounded as though the battery was dead.

Where did you buy the alternator? Charge the battery and have them both tested.

try hold up the key while starting, shot in the dark. if it startes remove extra items off key ring

check your alternator is giving out about 14 volts if no .check the brushes held on with two bolt behind your alternator as may be worn .or change the alternator.

Obviously the mechanic is not getting down to the real
issue for some reason
Try a different shop
I can only guess but it sounds like you may need
a new ignition switch & then the proper adjustment
if one is required
You may be able to dajust yours to work ok if that
applies.
Seems odd the mechanic spends all that time in one area
& doesn't have a solution
You may have a bad door switch as well

Sounds like your alternater, get a multimeter set it to volts start the car then check the battery is getting 14 or over volts from the alternater to the battery , if your getting less than that it's not putting enough volts back to the battery to run the car with good luck colin

Get the fault codes read first to get an indication on where you should start

Check the anti-theft module and relay

earth cable from body to engine and battery to chassis ,clean the connections and fit an additional cable ,also clean and grease the battery terminal

You could have a alternator problem. When the alternator stops charging the battery you are running on just the battery. When the battery gets weak a lot of weird things starts happening. Have your alternator tested.