Does mountain biking damage the motor?

Provided it's properly installed & maintained - no, no damage at all from trail riding, I do it myself quite a bit actually... you may find an occasional response lag as sometimes during the roughest bits the fuel gets agitated & the bowl hasn't filled properly, but that's rare & only one of my bikes does that (NT carb).

You also may find the stock 44t sprocket too tall for the technical, tricky bits on the trails... but ofc I just pedal those

Clean your air filter often, especially if you run through water, mud, or heavy dust conditions.

Don't bog it down (run it too slow).

i am flanging up a wheel with a 50 tooth to play off road.should work nice.
my lighter bike should handle it nicely.