[LS short box]

Sorry I maybe didn't say it very well.
You are correct on 1,2 and 3.
Two ways to do the fan or fans. Signal from the ECM or bung in the radiator with a temp sensor from a kit from Painless Wiring. I've used both with no problems. If you use the ECM to control the fan/fans you can fine tune the on/off temps to your application.
TCC? Not knowing what year LS you are using the earlier year LS (24 tooth reluctor crank wheel) needs an open from the brake switch to release the lockup. I've used a 2002 Camaro brake lite switch. It has two set of terminals on the switch. One open and one closed when you press the brake pedal.
Later LS ECM's need a closed switch sending a 12 volt signal to the ECM to release the lockup. On my 80 Camaro project I just spliced into the stock brake light wiring/switch for a 12 volt signal when you pressed the brake pedal. It's a 2012 6.2/4L60E combo 58 tooth reluctor crank.