Question 1 ....Whats the easiest , neatest ( and cheapest ! ) way to cut a
1/8" ( 3mm ? ) groove along the end - grain of a length of wood?

It suggests using a circular saw on the page that you linked to. That
would probably be as easy and cheap as using a hand-held router -
clamp all the shelves together then use the fence - unless you don't
want to cut all the way through... If you already have a saw and you
don't have the correct router bit, then the saw would be cheapest!