No it would change with the Player's Guide. They cannot use any effects when off the board unless you are told to specifically, so that would include rolling for resources.

a point was brought up in another group that if a character is already indomitable, they can't use the utility belt's counter ta ability because it also grants indomitable in the wording and characters can't be granted indomitable ability when they can already use it. is this true?

The only part of the trait that they will not be allowed to use is the indomitable, all other parts of the Trait will still work.