RIDDLE OF THE DAY

Two words, my answer is only two words. To keep me, you must give me.

You use it between your head and your toes, the more it works the thinner it grows. What is it?

The more you take, the more you leave behind. What are they?

As defendants, we deny all involvement in the unscrupulous dealings which have come to light in the recent government investigation.  What country name is hidden in the previous sentence?

I am weightless, but you can see me. Put me in a bucket, and I'll make it lighter. What am I?