Invincible AI ship?

My first game (tutorial even). I send a rather sizeable fleet (3-4 battleships, some cruisers, with basic lasers and nukes) to a star system held by the opponent, and defended by a single AI opponent ship.

The first battle round has that opponent ship down to 9%. I begin hitting hard (fast decrease in opponent ship health), then less and less hard. Orders were to close in as my weapons are most effective close range.

Next turn, it's back up to 56% (a starbase in the system healing for 47%????), and all my attacks just bounce off: I hit, with no effect. I also watch my battleships being shot down one after the other.

(1) In the battle or regular interface, can I check what ship, and what planetary defense my opponent has? Note that I've assigned over 20 covert agents to this AI opponent (which gives me a whopping 4.3% or so chance to spy successfully...)

(2) Are nukes one-time use only? (Only my battleships have nukes - 2 each, and 4 lasers, all level 1)

(3) What is going on?