This is a real can of worms this one. It's difficult to know where to start.
First of all, how did the bearing in the flywheel collapse when the garage were doing aircon work? I can't see any tie-up here.
Secondly, to fix the flywheel problem, they would obviously have to remove the gearbox.
Off the top of my head I would say that the garage has possibly not reconnected something properly (sensor connector, or transmission earth lead), Or more probably, they have damaged the crankshaft (
) sensor when removing and refitting the gearbox.
The onus really is on this garage that did the work. If the engine was running properly when the car went in, but now it isn't, well there you go.
I would seriously think about returning to the independant garage that came up with the fault code. Have them sort it and charge it all to the garage that did the flywheel job.
I know this will be difficult, but the first priority is to get the vehicle functional, then sort out who pays what.