Tell us about yourself!
Firewalls are the crunchy part of the Tootsie Pop, with the network behind it the qooy chewy center.VLANs help on sniffing & such. But this then becomes a nightmare for the typical hobbyist who would be building something like this. SSH is your friend.
A good managed switch would probably allow up to about 128 nodes. Or so.
Each node has its own unique memory. There's no combining the memory as each node is potentially running at a different spot in the program, assuming every node is identically tasked. Clusters (unlike "super computers") do not all have to be running the same code.
And if you get overwhelmed by the kids, you can a) toss down some of that vodka (so, do you buy the cheap stuff since you're not really planning on drinking it or the good stuff because you might?) or 2) pour a little in with the cream mix for the kids.This is a pretty neat idea. Actually very instructive on thermodynamics as well as fun.