First, I would take it back to the first place. They messed it up and need to see it through.

Second, it sounds like they may have pulled your axle for the bearing and did not set your axel in properly after so it was not making good contact in the trans which ate away the splines.

Third - Not really sure how this may affected the bearing though. If it’s a bolt in bearing they usually have 4 bolts and while leaving one out is not ideal, it should not have been an issue right off the get go.

The technical term for this is Bullshit

Yes, not uncommon. As oil heats up, moisture trapped in it will steam off.

10 minutes is way too long. Wait until the RPMs drop (choke is off) and you are good to go. Especially now when every car is using 0 or 5W weight oil.