Answers:
Both your wireless adaptor and your wireless router will "dumb down" to the lowest adjectives denominator.
A wireless G card will work on a "N" router, but will work at G speeds.
Same go vice versa. It wouldnt hurt to return with an N type router or card, as it will be organized when you are of a mind to upgrade the other, but you really won't see an growth, unless the architecture within the N router is inherently better than the G router.