Hi, David. We all had to start somewhere so just let us know what you don't understand and we'll try to explain. Thanks for doing your homework first. I try to write for the person that asks a question but that doesn't always work or help the reader that comes after.
As for the remaining stains, unless you start with wood that is basically the same color, the color variation will remain, no matter how you stain it. I would guess that the dark stains that you have were caused by animal urine but they are so old that they no longer smell. Shellac will kill the odor but do nothing for removing the dark spots. But then, they could just be caused by water too. So the process will be one of trying to get the dark spots out.
The best way to accomplish this is to first try household bleach on the spots. Put it on straight out of the bottle and let it sit for a while. Let it sit for a half hour or so and then rinse and finish with a rinse of 1 cup of vinegar to a gallon of water. Try to use as little water as possible on the floor and get up all that you can. If this did not work, then try Wood Bleach (oxalic acid) that is sold at home centers. Just follow the label directions. One of these things should work. Then let the floor dry thoroughly. You will have to resand any areas where you put water based bleach or water. And be sure to wear gloves and eye protection while working with any of these products.
Let us know how this is coming and if you have any more questions.