----cut----
To run it outside, I'll have to run the venting up into the about cabinet,
then into an inside an interior wall cavity about 24" (can I do this?) to
the ceiling. From there, can I run a flexible vinyl tubing to the roof?
I
am about 35" from an exterior wall. Which is best? (roof or wall)...

Howie

Mine vents up into the upper cabinet and then through the wall inside the
upper cabinet. Less than 24 inches total.

Check the directions for the maximum length of exhaust for you unit.

Flex is out, not approved for kitchen exhaust. Remember this is fairly low
pressure exhaust. Any obstructions/corrugations in the pipe will just
collect grease.

I once used a bathroom that had carbon filter. Yikes never worked.

I do not understand why anyone would want to recycle hot/greasy/humid air.
Look at the filter, do you really think that it is going to filter much? For
that matter the exhaust on mine does not really work except for the rear
burners. Makes more noise that anything else.