"If I took a picture from Wikipedia and incorporated it into one page on an existing website, what would I have to release under the GFDL for that inclusion not to violate Wikipedia's license? Would I need to release that page, my entire website, or neither (just the picture) under GNU FDL?"
I'll echo the "I don't know"s, and add a complication: pictures and text are a bit different. Almost all the text in Wikipedia was made collaboratively, and is therefore unquestionably FDL. But many of the pictures are either public domain or used under "fair use", so using them in another work would have no affect at all on that work.