Battery light comes on when driving

ok, check the battery leads are tight - maybe coming loose, this would turn the battery light on + make it cut out, run poorly etc.
key could be worn, get a new one cut possibly? OR lock could be siezed internally, oil the key, jiggle it in the lock...
the multifunction switch could have come loose - this will make it feel like the lock has jammed if it happens just right, check it by removing the cowl under the steering wheel and looking at the side (opposite to the key) of the ignition barrel - it is on the end of the ignition barrel shaft.
check the fan belt tension/condition?
check the battery itself, for low fluid, serious corrosion or swelling - replace it if any of these signs are present, but if it seems fine have it tested just to be sure before you THEN suspect the alternator - any honest garage should do this for free it takes five seconds! - tell them you think the alternator has had it, could they test it for you...

It's a distinct possibility they didn't tighten the drive belt sufficiently. This would cause the drive belt to slip and the alternator won't put out a sufficient charge to recharge the battery or drive your accessories. No idea why you have issues with the key in the ignition as it shouldn't be related to your battery light problem.

SOUNDS LIKE THEY MAY HAVE DISCONNECTED THE ALTERNATOR OR PULLED THE CONNECTOR LOOSE WHILE DOING THE CLUTCH.