a little...youll be able to apply to programs who do not sponsor visas but have some IMG as well so it expands the number of places you can apply to which theoretically increases your chances.
no, you are already a GC holder. it does not matter if you become citizen. they both have equal opportunities
dosent change anything if ur a GC holder already. Changes a lot lot if u need visa and now don't. Needless to say.