1. They gradually recover hp over time albeit very slowly. I believe starbases must have repair kits (construction ships) sent to them. Having ships in orbit repairs them much faster.

2. Sential watches only for enemy ships and guard watches for enemy and friendly ships that enter it's ship's range. As long as no ships enter their sensor range, they won't be awoken for you to bother with.

Actually in regard to repairing ships you can also do this far more quickly for a reasonable fee.

Just create another identical ship to the one you want to repair and name it something different like Fighter I and Fighter Ia. Then when a Fighter I gets damaged all you need to do is to "upgrade" it to a Fighter Ia. Since there really is no difference in these two ships the cost to upgrade is very reasonable, usually in the range of 100bc although this naturally gets more expensive for more expensive ships. Anyway as long as you're in your own area of influence the upgrade usually only takes one week and completely heals all damage. Don't forget that a ships HP is reduced to 1 while the upgrade is in progress.

What I do is to have a couple of fleets of my top line attack ship move together. As ships from the fleet I'm using take damage I remove them from the fleet and replace them with an undamaged ship. I then move onto the next attack where I do the same thing. Typically the final result of a string of attacks is that I've conquered a good handful of planets, so I park all my ships in the same parsec with a fleet formed of my undamaged ships and my damaged ships "upgraded" to repair them in 1 turn. The undamaged fleet protects the ships being upgraded and then next turn all my ships are repaired and I'm ready to do the same thing all over again.

Some people consider this an "exploit" or even cheating and if you're one of those then feel free to not use it. But I have no compunction about it and consider it a fair service received for a fair cost. You be the judge.

Yes. The paragraph is a bit misleading:

Starbases need repair kits sent to them.
Having ships in orbit (around planets) repairs them (the ships) much faster.

You are correct. Starbases still fix themselves, but only a point or two a week. Repair modules give 20 hp repair instantly.