Do they rescue Quynh in The Old Guard?

It's a dark moment, though it's built on the hope — however withering — that Andy can find her and restore their long-lost relationship. But at the end of the movie, we see that Quynh has, indeed, escaped her underwater metal chamber.

Does Andromache of Scythia get her immortality back?

This resulted in Andy's first death, after which she came back to life again and found she was immortal. She eventually became the leader of her tribe after defeating the enemies who killed her for the first time.