Ok. Auto conversion is fairly straight forward. Need Auto TCU and 95% chance that it will marry up to the ECU. The fact that there's an external TCU makes it a lot easier.
If you're tracking the car from time to time, the shift kitted auto will be a better option. Think the RE5 is the stronger box of the two from memory.
If you're defining 'feeling the gear change' as the feeling when the engine lowers it's revs, then that's kind of true. With an exhaust, you can hear/feel when the car drops from 4k-3k-2k.
Out of curiousity, what's your diff fluid like?
The trans cooler is an external unit not part of the radiator.