I'm trying to refinish my floors. My plan is to sand, stain to a medium or medium-dark brown, then poly.

I plugged all the holes, make little wood splinters and glued where necessary, etc, and solved all those problems. My one problem left is the gap in the pictures below. In the middle of a 20x20 room there is this decent size gap, probably 3/16" or so, a little narrower at ends, and about as long as my 4' level. It does close slightly during the summer (humidity), but it never goes away. All the other gaps i can live with. I can't cover this one with a rug.

So what are my options here? One person recommended mixing stain and my poly with my clean sawdust and packing the gap, letting it dry, then sanding down. I also see there are fillers on the market. I have a table saw and could try to come up with a splinter, but its gonna be hard considering that gap is narrow on the ends, and fat in the middle.

What's the best solution here?

PS. I have a couple black stains where some nails were in the floor and they got wet. Any solutions there? I tried hydrogen peroxide but maybe i didn't leave it on long enough...

Looks like there is more movement in that one area than the rest I can see. Could have there been a board replacement there before? If it is still dry in your area that may close up more in the summer but I wouldn't want it to fill with finish.