I am planning on installing approx 450 sq ft of Braz Cherry from BR111 here shortly.

Just wondering what I should use to fasten it to the floor.

Do you have issues with very hard wood such as Braz Cherry in splitting the tongues often? If so, how can I prevent or reduce this in my install?

What kind of nailer and fastener should I use.

Some guys swear by cleats, others swear by staples. I just swear when I have to do Brazillian Cherry. I use staples, 2" long, come in from the ends 2-3 inches, adjust the gun properly, and the air pressure on the compressor.
If you have a few splits you'll be ok. Some boards tend to split more then others.

With as little as you have to do, rent a manual cleat nailer, and don't worry.
Even less chance of splitting, and the exercise will do you good.

Will the manual do staples also? Anything to help avoid the splits like supporting the tongue?

No, the manual only shoots cleats, they were the standard for many years, and are still suitable today. That gun, will be the least problematic way for you to install your flooring. I doubt you will have much splitting with a manual nailer, if at all.

If you go the manual route try to find a powernailer one it's the best manual imo. THe ratcheting one might be good too for a rookie on BCherry.