1) Since there are only 3 tokens for drained domains does that mean the maximum amount of Domains that be drained per turn is 3?
There is no limit. You start the game with three domains, but it's possible to gain more domains, and also possible to refresh a domain so that you could use it more than once. If you run out of tokens, you can just use pennies, glass beads, or whatever else you have around to mark whether a domain is drained.
2) Can an ability on a character card be used at any time an action can be played if it applies? Even if the character is exhausted?
Yes. As long as you can pay the cost of the ability, you can use it during any action window. So, it does not matter that the character is exhausted unless exhausting is the cost that you would need to pay.
For example in the core set the Clover Club Torch Singer. Her action is to give someone -2 skill for a phase. Do I just trigger that? and Say I am doing it? Or do I have to exhaust her to use that action?
You just declare that you're using her ability, pay the cost, and it happens. Note that you can use an ability multiple times if you can pay for it, so if you have several domains to spend you can lower someone's skill even more.
Or how about PATSY. Sacrifice him to drain exactly two tokens from a story. I dont have to pay for that I just trigger it? I guess I am having a hard time understanding when you can trigger an action on a character and if you have to pay or exhaust or how its used
Same deal - you just declare that you want to do it during any action window, pay the cost (which in this case is sacrificing Patsy), and it happens.
3) When it says to "pay 1" to do something does that drain a whole domain? Also does the color matter?
Pay X means: Drain a domain with at least X resources. So yes, it does drain the whole domain. The color does not matter unless the card says so - and it's very rare that it does. For instance, the new Professor Nathaniel Peaslee card specifically says you have to drain a domain that includes a Yog resource.
4) When it says I can sacrifice someone as an ability can I do that whenever I want? I just kill them off and apply the effect?
You can do it during any action windows which is basically about any time except while stories are resolving. Once you start resolving any story, the action window is closed until all stories finish resolving.