Rep Power: 518

I dunno....
If you crank on the screw, the computer should increase or decrease the IAC valve position to keep the idle RPM unchanged and steady.

If the IAC valve is able to handle all idle load and temperature conditions, you shouldn't need to mess with the screw.

I mentioned it because I thought it was idling too low all the time, which apparently is not what's going on (misunderstood your complaint at first).
Randomly dipping way too low shouldn't be related to the bypass screw, because the IAC could handle it at any other time.

I thought the randomness could be helped by doing the relearn.

 
Rep Power: 210

Looks like my son's Mazda 3 has either spun a bearing or rod knock. It's past the salvage yard's 30-day warranty. It's been less than two months ago the engine was purchased so maybe the salvage will understand the situation and find another one without charge.

If not, the body shop/mechanic shop owner should be live up to his word and either rebuild or replace it.

It sounds very similar to this:

 
Rep Power: 518

If that was the car with the oil light coming on, that explains why the oil light was coming on.

/fork, done

 
Rep Power: 210

Unfortunately, yes.
Salvage yard is saying out-of-warranty and won't refund or replace. Body shop/mechanic will do labor free but, not responsible for engine. I'm disgusted but, I know the world of used parts and shady mechanics is some of the shittiest bowels of our society. Only positive is that it's a hard lessen learned for my son to always drive with caution, always be wary in business dealings and do as much repair as possible DIY.