A lot of your questions can be answered by looking back on Connor Hawke’s introduction/integration into the DCU.
The heroes would try and be accepting, even Batman, who’d be like ‘WTF Ollie, you nailed Talia? What is it w. you archers having kids w. female villains?”
He and Dinah would get through it, same as always. She (and the heroes) all know Ollie’s a horndog, and still love him, warts & all.
R’as would of course, feature more prominently in the GA mythos.
The interesting question(s) would be Damian’s take on things.
Would he really lower himself to sidekick for, or try and take up the mantle of whst he’d no doubt consider a B list hero, as full of himself as he is?
As for me, Damian made no impact on me when he showed up, but as a GA character, i would probably have been more interested in him, especially if what i wrote about his reaction to GA was actually happening.