no, no lining. all that'll do is hide the rust. if your car is leaking, it's already there ...
do the "crunch" test, remove the carpet behind the seats, and press down on the lower part of the ribs. if you hear it crunch, you got rust under the tar-mats ...
yes, those are tar-mats glued to the floor and painted in body-color.
they're a bitch to get out (heat-gun and scraper) and if you fail the crunch-test, you *will* have a lot of rust under there ...
Andy