Hi and welcome. Here are some additional answers:
I'd much rather use a linear polarizer because it has a much stronger effect than a circular.
That is not correct, the effect is the same. A circular polariser IS a linear polarizer with an addd element.
I know circulars are required for the auto focus on a SLR because of the beam splitter required for the optical finder.
A circular polarizer is required for autofocus with a SLR or DSLR, correct. But it's not linked to the optical viewfinder, which doesn't have a beam splitter. That beam splitter is in the focusing system.
Since the FZ18 uses an EVF will its' auto-focus work OK with a linear polarizer? Also: how critical is a thin polarizer for avoiding vignetting?
The EVF is not linked to autofocus, but yes a linear polarizer wil work fine with your FZ18. I'd suggest you get a thin polarizer to avoid vigneting, but the tolerances on thickness vary for each camera. The best thing to do would be to visit a store and ask to test a few polarizers.
Here is additional information on polarizers:
http://www.digicamhelp.com/accessories/filters/polarizers.php