DNA testing

Some questions about DNA testing.

If one took two donors’ samples of blood and throroughly mixed them togehter, would a lab be able to tell that fact and get a DNA profile of each donor?

I’ve heard of DNA being used to determine paternity. Can it go back any further? If I had a DNA sample of a person thought to be my great-grandfather, would a lab be able to determine whether he was, in fact, a blood ancestor?

If (George Orwell: eat your heart out) everyone’s DNA were on file in a database, and if I had no idea who my natural parents were, would a DNA test be able to determine who they were?