Nirth: When is killing allowed (not reducing reputation)? Do I have to be hit first for it to be counted as self-defense or does it depend on the attacker's status? If so, how do I see the attacker's status?
You may kill only bandits and burglars. The former look like...bandits, the latter have a certain burglary look about them and can be found in quarantined houses. :) Civilians will attack you if you steal anything from their homes. Don't retaliate, otherwise your reputation will drop.
Nirth: Where do I find water to fill bottles?
At hand pumps and water fountains dotted around the town. If I remember correctly, after a certain day the groundwater becomes contaminated so that few water sources will work. Look for bottles and fill them whenever you can – they're your most valuable currency.
Nirth: Also, how does exhaustion work?
Again, I haven't played the game in quite a while...do you mean fatigue, which gets worse in time and can be alleviated by sleeping? If you're out of time, you can chew on coffee beans, but they harm your health.