Is there any problem piggy backing the electrical hook-up to the fan via the Hunter "Ceiling/Fan & Light Control (27183) to an exsisting wall outlet.

I shouldn't think so. The control and fan want to see 120vAC, and if that's what you're giving it, good!

Is there any problem piggy backing the electrical hook-up to the fan via the Hunter "Ceiling/Fan & Light Control (27183) to an exsisting wall outlet.
i am building artifact display cases (4'x8')that require plexiglass lids. What is the safest, easiest, cleanest way of cutting sheet plexiglass
1/4"x4'x8'..