They are certainly allowed to defend themselves in a hostage or kidnap situation and I doubt any court would be hellbent trying to prosecute if the kidnapper was injured or killed.

I guess it depends on the exact situation.  You can't just off somebody and claim they were holding you hostage, then get a free pass.  There will be questions to answer.

And what if someone with multiple personality disorder threatens to kill themselves?  Does that count as a hostage situation?

Yes because it would be in self defence. I mean what are they doing kidnapping you?

The legal standard to kill a kidnapper is the same as anyone else, you can only use deadly force if you can articulate an immediate danger to your life or the life of another person. 

Certain countries have different definitions of what is and isn't considered to be self defense, its a tricky area to say the least!

In Canada where I live, a person cannot be convicted of killing another IF they believe serious bodily harm or death will occur to them, or to others. For instance if someone has a knife on you and its pressed to your throat and you end killing them with a blow to their heart, legally THAT would be self defense. 

Now lets apply your situaton here- What is occurring in the situation? Is the hostage taker attempting to attack others? Is he/she merley just holding a person(people) in a room and not allowing to leave but without being violent? It all comes down to intents here! If the hostage taker is physically trying to harm/kill others and you kill that person, it's self defense 100%, Now, if its a standoff, and you are merely killing that person to escape, it would legally not be self defense and you're looking at a 2nd degree murder charge.

Even in cases of self defense, usually the person is arrested and charged with 2nd degree murder/manslaughter! It's then up to the defendant to hire a good criminal laywer, and explain his side of the story, if it is self defense it comes out in court and charges are tossed.

It would depend on the specifics of the case and whether the police believe you responded with justifiable force to protect your life, or whether they believe you used excessive force.

If your life is still under threat up until the moment that you kill the hostage taker, then this would be a justified killing. If the hostage taker decides he wants to turn himself in and he lays down his weapon and is no longer a threat, but you then pick up a weapon and kill him, then this could be considered excessive since you could have simply walked away to safety at that point in time.

The hostage can legally use whatever necessary force is required to escape.

Note: You NEVER try to kill the abductor. You use necessary force to escape and/or prevent further injury to yourself or other victims. If that result in the death of the abductor, so be it.

Update to comment: Anyone with any sense knows that the victim CAN'T shoot in the scenario presented because even INCOMPETENT kidnapper wouldn't leave the victim with a gun.

That's an absolute yes friend when a person takes you hostage they are usually in possession of deadly weapons that's why you're a hostage. And you fear to resist because of a threat to your life. If you get the chance to turn the tables you blow the head off of your captor. Nobody is going to press charges on you

Yes, they certainly can.

Depends on the level of threat.