I just got my thief promoted to a ninja, and she is starting to get experience. I was wondering what skills to put my points into. In particular, is it better to have a high level sword skill, or is Kung Fu better? (I noticed that fists/kick don't do much damage, but I assume this improves with more skill points in Kung Fu, or maybe with higher strength.)

Kung fu is good as it improves your damage as well as to hit. I'm not sure if it is better to have a high kung fu or high sword with gallantry skill. Any more experienced ones want to answer this?
Also there have been reports of a kicking/2nd attack problem. I used a dagger/wak in my off hand and that seemed to work well.

You need to increase kung fu pretty heavily to keep the damage similar to that of two weapons. Advantage is you can use your off-hand for a shield (like the shroud), and still get a second attack. Disadvantage is you can't enchant your hands, and heavily blessed/enchanted weapons will be better than kung fu.
Still there is not that much of a difference not to try kung fu for a change, and it helps with money: you can sell expensive weapons, no repair costs and no expensive blessing-bills.