Batman mainly stays in the JL HQ as mission control and if he fights he wears one of the mech armor. Same with any Robins in TT except when they're supposed to be stealthy.
Robins wear thermal pants. They can be flesh colored.
The Justice League is divided into two teams. The Satellite team and the Hall team. The Satellite team handles celestial threats, the Hall team handles the terrestrial threats. It then divided further into two members team. The Hall pair is called The Brave and The Bold, the satellite pair is called World's Finest. This doesn't signify any authority over others, just a fun thing they made up.