"When you guys are doing all these multiple flushes are you catching and disposing of the coolant/water?"
Biggest problem with the amounts of antifreeze we deal with when flushing a vehicle cooling system is it can kill any animal that laps it up. If it just ends up in the yard it will be...
Ditto all above.
Here's a photo showing how to approach the engine block drain (1FZFE):
Here's a photos of a replacement OEM block drain cock, if your's is the original it will be a solid brass plug:
IME a busy mechanic generally doesn't have the time to do repeated cleaning/flushes...