I accidentally sold my shield generator
There's a buyback option on the vendor screen for the last two things sold there.
nowhere to repair, and choosing heal at a planet does nothing but repair my components
There's a few buttons at the bottom of a planet vendor screen: Identify All, Repair All, and Repair Structure (there's also one for repairing a single component, iirc). Repair All is just your components including your armor, Repair Structure is your green bar.
Your shields cannot be insta-healed by anything, but if you click on a friendly planet so it brings up the menu it should also give you a +recharge buff that speeds up your shield recharge. There's also "Ancient Recharge Stations" out there that do it much faster but are harder to find.
Trying really hard to like this game, but I'm not getting into the politics at all yet. How long before it gets good? Is this really just a boring beginning or is the whole game like this?
My first sector was weird due to some thing that made one race colonize everything really fast (hasn't happened again in 4 more sectors) ; it was fun at first and kinda boring at the end because there were just two races allied and it took forever to get enough +relations with the second one. Never felt bored after that.
It may be that this game is just peculiarly suited to me and to none of you. Some games thrive off of mentally filling in details, but having played Crusader Kings 2 recently I found that I thoroughly enjoyed it almost entirely because of mentally filling in details (it gave me mostly bare facts, but it just screamed that there was a real drama going on in there, great stuff), and I don't feel like I'm having to do even 20% of that in Drox and I'm enjoying it more.
But yea, helping a race in the early-4x-colony rush, making ruthless political decisions (I hope that boss finds you tasty, dudes, because I'm outta here! My allies will be by in an hour to clean up the scraps), making careful stat and gear choices to deal with a lot of interlocking dependencies to make my ship powerful enough to fight well, rejoicing when I find just the right piece of gear from a drop or a vendor, fighting for my life against boss fleets and knowing that whether I kill them or not matters
... I find all that really, really fun. As I've played more I've found myself wanting more (fleet fights with NPC allies are possible because they can send multi-ship patrols into monster or enemy space, but I want a lot more of that), but I'm happy with what's here.
If you're not, well, thanks for really trying to like it, and I dunno why our experience of it is so different... but I guess that's the way it happens sometimes.