Where are you located? Home construction methods vary from region to region. The kitchen prob never had hardwoods in it. If you peel the floor back far enough you would possibly find some kind of linoleum or asbestos based floor. I think I would try to get the lick-n-stick off of the left side, go rent a little puddle jumper machine from the local rental place and an edger and finish the floor. Even if you don't do a professional job it will look better than what you have. As far as the water stains go, just adds "character".

We are located in KY.

I did look into sanding and refinishing the floor myself. I just don't want to do a bad job of it lol. Now to help hide the water stains I could stain the floor a dark color. I perfer darker cherry colored wood anyway. But then I still have the problem of that gap and the different height floors.