The 2 large pieces would be the roof and the 2 isosceles triangles the gable.
I would glue the styrofoam to the plywood and cut them both together.
#2 or #3 plywood shouldn't be too heavy.
Sorry, but I don't understand the part about a door.
6. One roll of prime grade Duct Tape (not the inferior Duck Tape or such)
Gorilla Tape works great.
Gorilla Glue - Home