What a fabulous inheritence! Others have answered your questions pretty much the way I would. But never throw away a quilt or top because of a few stains. Someone less fortunate can always use a quilt, and working on it will be good practice. If you decide not to use them yourself you can buy a blanket and a sheet from a thrift store and use them for batting & backing to finish a quilt for donation.
And welcome to the board.