Falcon,
I cut blue foam with a box cutter (interchangeable blades).
I do the cutting on a piece of 1/4 thick glass with a straight edge.
I usually make the cut in 2 passes.
I mostly use 5 minute epoxy and high quality mylar tape for assembly.
I use spray contact cement for large laminations.
sometimes I throw in some gorilla glue for overnight stuff.
Ive been a modeller for 35 years and have not done any hot wiring yet.
I have been doing a lot of different vacuum forming lately.....

Here is some of the stuff Ken and I have come up with......