Re: Changing heads question
Mike, let's break this down into bite size chunks.
Is your counter top stone/marble, etc? If so, it's probably fairly flat, at least enough for a basic check.
Laid on the reso edge, if you're looking at two gaps directly opposite each other, they are the snare beds. They should be roughly 3" long and somewhere between 1/8" & 1/16" lower than the bearing edge peak/crest.
You mention the same/similar gap on the batter edge. That's not a good thing, but won't account for the big difference in head/hoop height from one side of the drum to the other. That's probably down to you tensioning the head unevenly.
What model of snare do you own? Is it metal or wood? Pictures will help us help you a lot :)