There is a type of glue known as Goop, which is your best bet for gluing leather to foam. A well stocked hardware store will carry Goop.
Use Elmer's Spray Contact Cement.
Poly vinyl acetate is white glue.
One type of glue that can be used when working with vinyl fabric is wood glue. Normal fabric glues are not necessarily strong enough to hold vinyl together, so wood glue is a better alternative.
If you use an all purpose glue or synthetic glue it should be fine.
We can't see the glue. -Name your glue- for a better answer.
If you mean the glue that hold the vinyl to the floor there is an alternative ask your local vinyl supplier about vinyl designed to be "loose layed".
You can find vinyl repair kits at your local auto parts store.
The vinyl liner should bond together with PVC glue from lowes or Home Depot. There is even a PVC liner that can be used with the glue to patch tears rips and holes.
Buy a kit that mends leather, it contains a certain type of glue that you have to use, and follow the instructions. you should be able to buy this kit either online or at a leather store.
Super Glue is not good on leather. I would use Shoe Goop or E6000 for leather repairs.
No, it wouldn't work as Gorilla Glue swells. It would be better to use vinyl tile glue or spray contact cement