The floor doen't appear to be sanded thoroughly. You need bare wood for stain. It won't penetrate old finish. See if you can find a Varathane EZV floor sander. It's a rental unit and, I believe, the best for a DIY floor job.

For the water stains you might try oxalic acid. It's available in hardware stores. Follow the directions carefully.

Minwax Polyshades is a tinted polyurethane. It's difficult to get an even color with it. Multiple coats will obscure the grain. Is there any reason you didn't want to use a stain and clear poly? If the floors sanded correctly only one coat of stain is necessary or useful. Also I would think that a stain as dark as Bombay Mahogany would do a pretty good job of hiding the water stains after you lighten them.

I can't tell about a color match without seeing it. You could try your stain on a small area near the kitchen. If it doesn't look good then sand it back off and get another stain.

Good Luck

I second the motion to skip the Polyshades, for exactly the reasons that Jan9 says -- difficult to apply evenly and heavy pigment obscures the wood. All-in-one finishes sound better than they work. An expert friend of mine calls it, "The worst thing to happen to a can."

You are going through a lot of work -- get some professional grade products and get good results.

Here is a link that might be useful: Floor refinishing video from Popular Woodworking / Cabot stains