I've also had Red fulltime at the Penthouse.  To him, he doesn't really have any other place to go that feels like it could be a "home".  Even despite (as yet unmentioned) reconnecting with surviving family, and forming a closer relationship with his "brother" Red Tornado in the missing past two years - we'll see that later!

The Justice League are aware of him, as such, but ironically him being human actually makes them (and particularly the Batman) [b]MORE[/b] wary of him and the possibility of his being a brainwashed Manchurian Candidate-esque mole than his "brother", despite his vouching for him.

Because it's one thing when you can access someone's source code and [b]SEE[/b] that all the evil is gone.  People are more complicated. 

Still, he keeps working, and intends to make the most of any opportunities to do good that he gets.

He's never sought out formal education and doesn't see the value in it, valuing knowledge itself and the never ending pursuit of knowledge over any piece of paper an organisation would give you for it.

As [@spicykvnt] mentioned, I view the two years they've kind of been thrust upon each other as doing wonders for their communication and platonically (after Red became desensitised to his own torrential hormones) forged bond.

I could see Kali making use of Red as a viable sparring and training partner though.