FTL Faster Than Light – Does the Clone Bay Regenerate Crew Health When Waiting at The Last Stand?

From personal experience (which seems backed up by this thread where the developer responded), the Repair Arm heals you 1 hull point, regardless of the amount of scrap collected.

From the developer via that thread as well:

We didn't want it to be always a positive, obvious choice. The power of constant repairs after every fight is too useful without at least a few setbacks. [...] I might sell it come sector 6 or 7 if I'm doing well since that 15% starts to hurt a lot more and the extra boost to finish off the boss is helpful.

The FTL Wikia seems to agree with this as well:

Repairs your hull by 1 point every time you collect scrap[.]

No, whether or not you jump out early has no effect on the delay of the rebel fleet in the next sector, therefore its to your benefit if you visit as many locations as possible in each sector.