You can do a burn test on small scraps to determine the fiber content. Now I don't know what the smoke or the residue on true cotton looks like, but synthetics will curl up (I think);
If you want to make a regular pieced quilt, I would recommend staying with similar weight fabric. If you want to make an art quilt or a crazy quilt, you can use foundation piecing and really - anything goes. If you want to use the thinner pieces in your regular quilt, you can back them with an interfacing or a foundation stabilizer and use them anyway,
A lot is personal choice.