CAN THIS BE USED ON A ROOF DECK THAT IS FINISHED WITH A RUBBER MEMBRANE? WILL THE DECK TILES PUNCTURE THIS MEMBRANE?

Yes, although the chance of puncturing is low, you may want to place an additional TPO or EPDM membrane / polysheet above your existing rubber membrane to avoid any damage during the installation process. We recommend a minimum thickness of 40 mils. We do not have a recommended product or manufacturer. The deck tiles themselves do not have any sharp points on the bottom. The bottom of the deck tile can be seen here: https://www.newtechwood.com/blog/product/deck-tiles/