Ok, if the files and folders in wfcache/ are gone, then there is definitely something else caching the pages. The clear.lock file is normal, too.
Yes, it is possible that W3 Total Cache didn’t uninstall completely — I think it usually leaves some folders behind, but shouldn’t normally keep showing cached pages. The best place to check is in the .htaccess file for the site, which would have code to load the cached pages.
If you’re not sure which parts of the .htaccess file are from W3 Total Cache, it might be easier to temporarily disable Wordfence’s caching, install W3TC again, clear all caches to remove any old files, disable all of the cache options, and then disable W3TC and turn on Falcon again.
-Matt R