I assume I need a flat head carriage bolt? Do I need to countersink the head into the control panel so it's not sticking up?
Those are really personal prefernce type questions. If you don't want the bolt head showing then, by definition you must counter sink and the bolt head style is really irrelevant (although I think a round head carriage bolt would be very hard to countersink in 3/4" wood). If you want the bolts to show, then pick a bolt-head you like because . . . well, it will be showing!
I notice the Happs trackball has a mounting plate that sits on top of the CP. Should that be recessed as well to be flat with the CP? Or do you leave it sticking up above the CP?
Again, personal preference. If you think on top looks weird, then recess it.
Will the CPO cover the carriage bolts and trackball mounting plate sufficient enough that I don't need to recess them? Or if I don't recess them will there be bumps in the CPO?
Maybe I'm not understanding you, but if you lay a CPO on top of bolts-heads that are sticking up, you most definitely will have large bumps showing.
You want to apply your CPO to a flat surface, so you'l l want to recess the bolt heads.
I have 3/4 in CP cover and 3/4 in tmolding. If I put tmolding around the CP, when I finally add the CPO will it still look ok? or will it be too think to look correct with the 3/4 in tmolding?
What is a 3/4" CP cover? Are you saying that you are puting a cover on 3/4" wood? If so, CPO's aren't very thick so molding will look fine.