If you buy a sheet of strofoam and walk down the streen with it in California, the tree huggers would beat you with sticks because of all the bad stuff produced when making styrofoam. No wait, use of sticks would promote the killing of trees, they would use plastic clubs. No wait, plastic clubs would promote the use of fossile fuels, they would use bricks. No wait, bricks would promote the mining of clay, thus disrupting the fragile ecosystem and displacing millions of rare frogs into homelessness, not to mention the possibility of interfearing with ancient burrial grounds, they would beat you with wet noodles. No wait, what about the starving Ethiopians? They would use, well by the time they decide, you'll be home with your foam.
I believe it's not safe to hot wire/knife strofoam. Blue/pink is safe, but should be done in a well ventilated area. If the temperature is right, it will produce little or no smoke and makea cleaner cut. You can make your own from nichrome wire or buy one.
I use carpenders glue, because menards has it by the gallon.
I use tooth picks to hold foam parts together as it dries.
I use drywall nails to hold foam to wood until the same glue dries, then leave them in unless I don't want to, then I unscrew them. They work well for foam to foam too, but I usually remove once dry because the hot wire has trouble cutting thru a screw
If I really couldn't get blue/pink foam, I suppose I would try styrofoam. Naaaaaaah, I'd move.