Cooling : car CAME WITH http://www.frsport.com/R0181-53mm-Aluminum-Racing-Radiator-86-88-RX7--FC3S-early-_p_1724.html This is adequate, correct?
Power steering : The power steering in it leaks, depending on issue, might remove altogether? Advice?
A/C : Not worried for the time being, it is a functional convertible
Exhaust : already has dual 2 1/2 or 2 3/4 all the way back.
Fuel system : Dropping in a walbro 255 for starters. Should do for now, Advice?
Shifter : IDK yet, prolly a junk yard pull outta something. It's a 5sp right now, going auto. Suggestions?
Gauges : Psssh... foot to the floor til I run outta room. (lol, will do integra speedo)
I don't think your stock location radiator will clear the bottom pulley on the LS motor.
I have AC in my vert, but I don't use it that often. The verts are not nearly as fun to drive with the top up.
Double check your exhaust. If it is still the rotary exhaust, you will have to add a lot. Are you using headers or stock exhaust manifolds? Headers are expensive, so stock exhaust manifolds are the budget approach.
Fuel sounds good, there are plenty of variations of plumbing that people have done.
Going from manual to automatic shouldn't be difficult. Look at what others have done for shifters, and an Automatic pedal assembly should be easy to find, not that you really need to remove the clutch pedal.
Good luck with the build, give me a shout if you have vert questions.