I'm enjoying the game so far, after finally getting out of the Privateers Hold alive, but the wiki doesn't explain how to do a lot of things.

How do you Repair weapons? Do you just leave them with the smith and come back later?
How do you pick locks, or find lockpicks?

Yes. Leave with a smith.

No lockpicks. Go into "steal" mode and click on the door. If your lockpicking skill is high enough the door will "click" open.
BUT....You only get 1 attempt, repeated clickings will do no good. If you're in town a second attempt will probably bring the guards after you.

The cheapest open spell (join the mages guild to get the best spells) will open any outside door in the game. Inside doors and magically held locks will usually require a better spell.

Yea, armorers will repair items for you, just talk to them. You'll have to leave the item with them for a few days.

Pressing F1 puts you in steal mode, which clicking on doors will allow you to attempt to pick them. Just be sure you go back to grab mode F2 before talking to someone, or you'll try to pickpocket them instead. I'll warn you though, that lockpicking is pretty lame. You often only get one chance to pick a lock, and it's a hard skill to level. Luckily, there is the open spell and you can even bash in doors by attacking them.