New 2 sport...quetions about fat tire division

not sure what you mean by 'fat tire division'.   I will tell you that you will be fine racing on your mountain bike in pretty much any shorter distance race.   I have done 2 sprint Tri last year and in both there were plenty of mountain bike riders, some even in the top 20% overall.   Just a working bike is all you really need, but you can gain some speed by switching to some road slick tires on your bike.

If you mean off-road Tri races, then you are probably good to go.   

Get fitted, the on-road riding position may be different than the off-road.  You can afford to raise the seat a little higher and the handlebars a little lower if you don't have to shift back and forth around the seat.  (I know, cyclist call it a "saddle" not a "seat" but they also refer to that element of the geometry as the "seat-tube"...)

The slicks have already been mentioned.

Make sure you have a suitable helmet. 

I did my first two tri's (sprints) on my mountain bike, no change of tires or anything (but my tires have a road-rib down the middle, so they were pretty pleasant to ride on asphalt).