Generally, training is paid at your previous rate.
New pay rate starts on the day you are converted.
They often do "mid-month conversions". ie= if you finish training on Nov 15th, they can convert you on the 16th and give you an IOE on the 17th. It will appear as MMC on your schedule.
It can also happen that you convert before you are even done with training. (occasionally before you even start training) They do that because of the seniority rules for conversions and because it is cheaper than pay protecting other pilots senior or junior to you. Its a rare good deal. Just like a paid vacation. Doesn't happen as often as it used to because the contract now gives them a 60 day buffer for conversions out of seniority.


On your 2nd question:
Once you set foot in the schoolhouse for 737 training, your M88 qual goes away. You will not go back to fly the M88.

One more detail -- if you convert mid-month or otherwise haven't been qualified to bid under PBS on your new jet, scheduling will give you your choice of a reserve line or a blank regular line.