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The yellow stain on your kitchen floor is likely due to the rubber backing on the rug altering the finish on your flooring. You may not be able to remove the stain without stripping the wax and recoating the floor. Before getting that drastic, try making a baking soda paste, with baking soda and water, and applying it to the stain. Allow it to sit overnight, scrub and rinse. You could also try hydrogen peroxide on the stain, or a weak bleach solution.
I tried all of the above and none of them worked. Then a friend told me just to let the air do it. I had removed the rug but had replaced it with one without a backing as looked unsightly........so I took that one up as well. At first I thought that nothing was happening, then noticed it was slowly getting lighter and lighter. She was right... after about 3 months there wasn't even an inkling of yellow remaining.
Baking soda worked fantastically.
I hope this works. The stains are ugly, but I like cozy look of having the rugs in place too.