It depends.
Some brand's ESC with built-in BEC are pretty robust and built to protect themselves in the event of a motor failure.
Some - less so.

The problem crops up when one of the output transistors dies.
When that happens, the LiPo battery is effectively directly connected to one set of the motor's coils.
Like a short circuit in the house, this will (literally) burn out a wire in the motor and may cause the ESC to catch on fire.
The original damaged motor could have been what caused the ECS to initially fail. Maybe it stalled while at 100% power. Or overheated. Or the metal can shorted against a coil wire.
But, once the ESC was damaged, plugging in the 2nd (good) motor cause that motor to fail.

Personally, I would trash the bad ESC and not worry about trying to reuse the "spare" BEC.
It may be a ticking time bomb waiting to fail at some point in the future.

As for future use of the 2S & 3S LiPo batteries, they should be ok.
As long as they are not physically damaged, they are pretty tough.

For helicopters, I've heard terms for LiPo pack damage like:
Taco (the pack is bent around such that it looks similar to a taco-shell). This is really bad. Watch for smoke.
Banana (slightly bent) - if it isn't smoking and it tales a charge, we fly it.
Pug (looks like a Pug dog's nose - flat - like the dog hit a wall going 50mph) - This can be worse than a taco. Best to take it out of what's left of the airframe as quick as you can and set it on a concrete pad away from anything flammable. Fireworks will commence shortly.