Why is VLC verified every time I open a file that is supposed to open with it?
If your Applications folder doesn't contain VLC.app, you probably didn't install it properly. The verifying process (trying to start VLC) indicates that a dmg containing the app has to be opened.

Since VLC is a self-containing app you don't have to initiate an installation. Instead open the downloaded VLC.dmg, drag and drop the VLC.app inside the mounted dmg to the folder /Applications. Then unmount the dmg and start VLC.