Across the room is fine, just don't handle the new one and then go over and handle the one you already have.
I have never had a female die on me from breeding, it does happen, but it's very rare.
Breeding season for most is upon us now, so no, it's actually a bit early for many.
But by the time he's out of quarantine you'll be ready to go.
I would start by offering the female more meals to help her gain the extra weight she needs to grow healthy eggs.
This time of year before my females start pairing up I offer meals twice a week if I can, and they happily take them for the most part.