just keep in mind that when you replace just one tire on a 4x4 power train that the tread depth on the other tires must be over 6/32 if not you can cause damage to your transmission. Being in th entire business for a lot of years you must make sure that you have the proper tread depth. I have seen this happen on several occasions over the years. Do yourself a favour and take it to a reputable tire dealer and they will explain how it works. As far as your tire goes, the sidewall is compromised and you can be assured that if you leave it on that it will blow out.
I think this used to be the case, but is not true for most vehicles with all-wheel drive today. At most, it will cause slightly more wear in the differential when using 4-wheel hi or low
To be safe, put the new tire on the front axle, but I don’t think it will make much difference. Now maybe if the new tire has 17/32nd and the old tire has 5/32... On second thought, not even then. The difference in rolling circumference between those two is less than 10 revs per mile...
I have an AWD wagon with a permanent 40/60 split, and that car comes with different diameter tires, front to rear...and the spare is a folding-sidewalk donut of yet a third diameter...