Capitalship Manual Cast isn't a problem for me
Then you're fine.
I would still likely leave Autocast on when clearing out an asteroid or a planet with only 4 militia
If you're not worried about depleting your antimatter, then most of the offensive abilities (like radiation bomb and nano-disassemblers) can be left on autocast. Hard to screw up an "attack the enemy" ability.
That said, a good strategy is to single out the siege frigates defending the neutral planets. Once the siege frigates are destroyed, you can sneak in a colony frigate (or better yet, just use the colonize ability on a capital ship) to capture the planet, then build a turret to kill the remaining defenders!
Actually, how exactly does that ability work, the stickies on this board aren't totally clear. I gather you cast it after a cap ship blows up, and the next cap you build has that ships level
Yeah, the ability's functionality is poorly explained, and you don't have it right. If you lose a level 6 Halcyon carrier, you can use this ability on another Halcyon to instantly promote it to level 6. You can do this as many times as you want, and if you have five other Halcyon carriers you can promote them all to level 6.
On the issue of placement, I know, for example, that my ships are annoyingly happy to engage starbases even when unnecesary
You can change your fleet behavior to "local area" targeting or "hold ground" targeting. I usually put all my units on local area. This means they will only attack units that get close to them, and won't attack something on the other side of the gravity well. The catch is, if you want them to attack something on the other side of the gravity well you have to order them manually. Trade-offs either way.
Are there any ships that recognize that they have port / starboard / aft weapons and maneuver to use them
Illuminators and flak frigates are the only standard combat units that fire any direction other than forward. Flak frigates are pretty simple: just put them in the middle of your fleet and they'll shoot down any fighters with little to no management on your part. There are entire articles written on tactics to get the most out of illuminators, so I can't exactly do justice to them with a short reply. The golden rule with illuminators is to make sure all three beams are firing. If they aren't, try moving the illuminators around; even rotating them slightly will cause them to acquire new targets.
Of all units to command in battle, fighters and light frigates probably are best worth your time. Both these units die very quickly (to flaks and long range frigates, respectively) but are also quite fast, so it's usually a good idea to keep them out of harm's way, and that usually involves keeping them moving.
