Well I can only answer 1 of the questions, and take a stab at a second.
For oil, some engines specify the type of oil. I have an 8.2 DD and use the Rotella T diesel oil. Coolant is the standard coolant you buy for your cars and not sure about transmission fluid, I have not yet considered looking into my AT545 or changing the fluid in it. I have read where people have used the standard level III transmission fluid and had problems. I would google the transmission specifically and you should find a ton of info.
As far as starting it all depends on the weather and such. I tend to idle it until it stops the wavering, which is usually around the time it stops smoking, so on a nice 40 degree F day this could take 5-10 minutes where on a 70 degree F day this takes all of 30 seconds.
Just out of curiosity why are you looking at a transmission cooler? I mean these buses have been running for 20-30 years and built to handle stop and go driving full of kids, if that doesn't heat up a transmission I don't know what does, so unless you are planning to do a lot of towing in Airzona in the summer, I don't see where a cooler would benefit you for the cost and work of putting one in.
1988 Chevrolet S6000 8.2L Detroit Diesel