Can I locate the parsed and plugins folder outside the web root?
You can, but only if you move all the directories so that they stay relative to each other. The directories “fusebox5”, “lexicon”, “parsed” and “plugins” must stay at the same relative position to each other. If you move the files, make sure that your index file correctly finds the fusebox5 directory and the circuit definitions in the fusebox.xml file correctly find your circuits.