If so what happens to the card forcing yuo to exhaust (if it was a plot twist, or another character activating)

It depends on the card, but essentially it has no effect.

[edit=brainfart]Removed bad example.[/edit]

While the effect is on the chain, you may respond by using activated powers or exhausting characters as payment for effects.

In specific example

I play a senitnel deck, and a friend of mine plays a doom deck

one of the Doom Army cards says something along the lines of activate -> Exhaust target character with a cost of 2 or less

As he's learned to fear Sen. Kelly he'll exhause his Character to exhaust mine,
Do I have still have time to Activate Kelly before he exhausts, thus not only accomplishing my goal of exhausting Kelly and hitting him for endurance, but also he essentially "looses" that army card (for the turn, as it is exhausted)?

sounds like from what you guys are saying, I would be able to activate Kelly, and since his army doom does not specify that it has to be done on a ready target (although it would be kind of silly to exhaust a non ready card) he would stay exhausted, but if it said "exhause ready target" then his would "re"ready

Robot Sentry cannot stop Senator Kelly from using his payment power. Robot Sentry may target Sen. Kelly whether he is ready or exhausted. When the effect resolves, however, if Sen. Kelly is exhausted, the Robot Sentry will resolve without effect. If Sen. Kelly were ready at the time the power resolved, he would become exhausted.

I've experienced the same type of thing with Dazzler and Puppet Master. The opponent controlled Dazzler and activated her power to exhaust my Puppet Master. I activate Puppet Masters ability and the opponent would then needed to exhaust an ADDITIONAL character!

So I ended up with him exhausting two characters to my one!

Dazzler cannot stop Puppet Master from using his payment power...

Tim

for Puppet Master, you cannot use an activated power to stop his power because his power says, 'Target opponent exhausts a READY character he controls." so if you exhaust a character before his power resolves, then you have to exhaust another ready character

UNLESS...

you do not have any other ready characters. then that is okay. but for example you have 4-drop human torch and 3-drop thing, he activated Puppet Master, you respond by activating Hotshot so he takes 5, you still have to exhaust Thing because Thing is still ready and you have to exhaust a ready character. but if you only have Hotshot and you exhaust Hotshot then that is okay.

now, if it is something like Mystical Paralysis which specifies a target, or Magneto 5-drop, then you can respond by exhausting your character as payment for an effect, then he exhausts your already exhausted character. that is okay,

Ok heres is another Situation

I have a robot sentry out and a Dr Doom and a Latveria

My opponent has a avalanche and another BH guy.
He exhausts Avalanche to blow up my Latveria can the Sentry stop him??

The Sentry could Stun Avalanche, but it would not prevent Avalanche's destruction of Latveria.

yup, i don't think there's anything, except for the utility belt, which will stop an activated power. as in the rules, once the effect is in the chain, it exists in the chain independent of its source, so once Avalanche uses his activated power, there's nothing you can do unless you use an effect like the utility belt's that negates effects.

The other option is to KO the location yourself or turn it face down, both through powers/effects. (I think this is legal for resources since face down resources are not considered locations/plot twists, even if they were face up once already)