If the thread is dry and brittle (the breaking test should determine this), you can revitalize it by placing it in a plastic bag in the freezer for a couple of months. This restores moisture to the dried-out old thread. Test it again afterwards, of course, to make sure it has become as strong as new thread.
I think the burn test is the only way to determine if thread is cotton or polyester. If you hold a match to the thread, poly should melt into a blob while cotton should turn into ash.