1. There are three possibilities here. I've listed them in order of descending probability:
A. The fighter's pilot is very experienced. Ships in GC2 have an experience/level progression system, and high-level ships are far, far more dangerous than they first appear.
B. The AI controlling the figher is very, very lucky; damage numbers are random, so it's theoretically possible for it to win that many fights.
C. It's a bug.

2. The AI never surrenders to any player. I heard somewhere that they surrender to the person in second, but that may well be wrong. Only Stardock knows for certain why the AI surrenders to who it does.

1: Check the amont of hit points, they might just be beating you down. Also, check to see if they have any military starbases around.

2: You can get a Hall of Empathy, that might help. The AI surrenders to who it does, sometimes you win, often you don't, that's just how it goes.

On the surrendering. Not sure if it is fact or fluke, but I went through a period where I would give a civ. a few old ships or something when they ask for help. It seemed to really up my chance of them surrendering to me, as I had it happen several times while using that strat.

Did you perhaps use a freighter hull as the base for your ship? If so you would only have 1 hitpoint which makes it quite likely that you would lose to a enemy fighter, even a much weaker one. Also I second apoc527's statement, multiple weapons types is generally bad, as is multiple armor types. Sepcialize your ships to beat a certain enemy and the game becomes a cake walk.

Ditto for weapons...which can greatly affect defense tech strat. This is why I love this game... it is never as easy as it sounds.

Any given ship should be focused entirely on one type of offense, at least from what I understand. Do extra attack types mean extra attacks, or is it lumped together and the sum is applied against the defense just once?

If they have any defenses at all and assuming each weapon type on a given ship is treated as a separate attack.. then your ships are hideously nerfed.

Really, a 'standard fighter'? What the hell is that? It depends entirely on technology, could vary anywhere from 1 offense and 0 defense to 20+ attack/defense.

Did they have a military starbase (or several) in range?

Were your ships in range of one of your starbases when you checked the stats (and not after you attacked)?

Hi!

From one weapon type with all three defenses, to two and three weapons with only one or no defenses. It depends on the situation and my "creative muse".

Your "creative muse" is pretty right. There are situations when any combo works. Like:
- AI using lots of undefended small ships with low attack (early game, AI using heavy fighter with attack 1-3): use any defense, and 1, 2 or even 3 types of weapons. The reason behind many types is each weapon type rolls separately, so you can hit him 3 times for at least one point of damage each hit (weapons roll form 1 to max attack). The reason against that is when AI starts to put on ships defenses, your low-attack ships became much less dangerous.
- AI using lots of small lightly defended ships with low to moderate attack (late early game, heavy fighter with attack 2-5, 1-2 defense): use proper defense to block most damage from his average ship, and only one type of weapon. Since each weapon type rolls against existing defenses it is better to attack with single high number, increasing the chance most damage will get through that small defense.
- AI using small to medium ships with good attack and moderate defense (mid game, heavy fighter with attack 4-8, of frigate with attack 4-12 and 2-4 points of defense): use medium or large hull with lots of defense (100-150% of his weapon attack strenght), and one type of weapon, preferably the one he hasn't proper defenses for.
- AI using medium to large hulls with very good attack and good defense (late mid game, frigate or battleship with attack 10-30, 5-15 defenses): use large or huge hull with lots of defense (150%+) of his average ship attack strenght, and one type of weapon he hasn't proper defenses for. Have as much firepower in one ship to kill 2-3 of his average ship + its defenses (he has 35 HP and 15 def, you need 100-150 firepower), almost assuring 1 shoot = 1 kill, thus reducing damage your ships take in combat.
- Late game (ultimate weapons reached). What will I use depends on the situation. In that time frame (quite rare in my games ) I'm usually so big nothing matters anymore, so I keep using defenses. In case AI would field fighters (small hull, 100+ attack) I would consider "interceptor": small hull, (cheapest) attack 20-30, 2-3 engines, nothing else. The trick is he'd spend much more in useless big attack strenght against my "cheap" interceptors.

My 5*2 cents.

BR, Iztok