Is there a CR adjustment for adding an ability to a monster? For example, if I just wanted to add regeneration to a Dire Boar?
A Giant or Advanced trollhound comes pretty close to a dire boar, I think regeneration or fast healing 2 or 3 should be ok, if there is no template best thing is to compare it to somewhat similar monsters I guess. Alternatively you can see if giving them PC wealth magical items can do something similar so you can estimate if it is within reason. (PC wealth should normally raise the CR by +1)
No, there isn't.
I had a similar thread on generation of pcs. Azlantians get +2 to all stats so it is possible to get 20s across the board...I've come close.
The best answer I could give would be to recreate the critter using the Advanced race book.