Hi Rita, you've presented what we like to call in the trades "A Doozy!".....
Reviewing your complete thread (and screen shots - REALLY NICE JOB with those) and trolling through the Evernote forums AND searching Google and Wikipedia for similar issues has been less than telling.
I think I may have a path for you to follow, but it's based more on intuition than fact.
If your original install was from the App Store, it sounds like there may be some history in the Evernote forums of a possible conflict that is reconciled by replacing the App Store installation with a direct download of the latest Evernote version from their website....short of a full nuke and pave reformat and reinstall from scratch for your complete System and User info on your computer, I'm thinking you might want to install Evernote (again) from the direct download and then follow the guidance in
this post from the Evernote Forums to remove it and the data completely.
It seems clear to me that your prior piece-meal removal process left some legacy hidden component....the process above should properly overcome that (I hope).
Just remember, that when you go to install from any other source than the App Store, you will have to go into the System Preferences Security prefpane and allow the install.....
Good luck with this one and let us know.