We haven't established answers to these questions. My instinct, though kappa may disagree, is that there is a single genetic marker for bending and you can wish one but only one; the Avatar Bell is genetically an airbender and her ability to do the other three is a spiritual matter that would be less readily wished. Bending will work in other worlds unless they share that inconvenient property of the spirit world.

Questions like this might better belong under the How To Read Effulgence thread, since characters don't currently know the answer.