what glue can you use to....

glue rubber/vinyl to each other and to a cardboard? It’s a foldable mat made by lemax and some people say it is made of rubber and some said vinyl. Can you also paint on them with acrylic?

2 part epoxy

Ditto on the epoxy. Super glue might work (it’s easier to try that first), but the epoxy will probably be your best bet.

Maybe this will help :

Super Glue will work as long as whatever it is stays flat .If you flex it ,fuggedaboudit ! I would go the two part Epoxy .Look around ,there is an epoxy product for rubber/vinyl .I don’t know what it’s called though . T.B.