When gluing fabric to foam, you want to be careful not to damage the fabric. For example, applying glue directly on a piece of fabric may discolour the fabric. It's best to use a fusible interfacing ...
Gluing wood and foam can be extremely tricky--the foam's absorbent nature makes it difficult to glue, and some glues can even cause the foam to melt. However, using Polyurethane construction adhesive ...