Glue should most likely not be used at all. It would be best to call a tack store and ask if they know of a Saddler who could repair the saddle for you. It might wind up being more expensive, but at least the saddle will be usable and correctly repaired.
There is a type of glue for every repair.
A good epoxy .
You should use a special type of glue called "craft glue" or "foam glue" that is specifically designed for bonding styrofoam. Regular glue may not work well with styrofoam.
No type of glue should be used on seat belts.
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.
You should use fabric glue on fabric for the best results.
White glue , Super glue . Leave it for about a few minutes for it to dry
Silicone.
You should use a craft glue or a specialized foam glue for foam sheets. Regular glue may not adhere well to foam.
Liquid white glue should help. If not, then I have no clue.
You should use a special type of glue called acrylic cement or solvent cement for bonding acrylic plastic.
You can find the type of glue you need at the upholstery shop. They will be able to advise you on how to make the repair you need. It will probably be a good idea to use both a foam glue, and some upholstery tape to hold it together.