I've found "rubber shorts" on amazon. Many are made of spandex (some 20%, and 80% nylon or cotton). Is this an effective alternative to dental dams?

Nope. If you are trying to prevent an std, you need material that prevents the transmission of even very tiny microscopic bacteria or viruses. If the product has cotton in it, it is not likely going to be an adequate barrier to protect from stds.
No. I would have to see the reference but this would be a new one for me.
No. To provide an effective barrier, dental dam material has to be totally impervious to liquid.