You could try seeing if its protocol handler was set properly. Open the settings app, and use the serahc box to find "protocol" and open "choose a default app for each protocol".
Then here see if you can find the appropriate protocol for evernote. If it's not there but should have been added by the evernote installer then something may have gone wrong with the evernote installation.
Why this warning notification isn't present in Firefox on the same sites? Is it some false warn in Vivaldi?
Probably it's because Mozilla (Firefox's maker) maintains its own security certificate store that is used by Firefox for https authentication, whereas chromium-based browsers like Vivaldi rely on Windows' certificate store for that. It sounds as if the Windows cert for the site perhaps has not been included or updated in some way like the Mozilla cert may have been. In that case, the Windows cert(s) need to be updated, or cert-updating turned on in the OS if it's been turned off.
Based on the few suggestions you've made for me I think we've saved my library!
Steps I took (They aren't perfect, but I tried to adapt)
So, what I did was I took my backup "Default" folder and put it in One Drive. Renamed the Default folder I had in Default User. Ran Vivaldi 11.97, imported from Vivaldi and immediately exported it before closing to a new bookmark and settings export. Uninstalled Vivaldi. Installed Snapshot build 12. Used the HTML that was most recently updated and from there worked all night on pruning duplications of bookmarks and what have you so that by the time I worked on updating thumbnails, I was working with a clean library.
I know the method is very flawed and round about, but that's what I did thanks to Ayespy's advice. If anyone is having problems with their Vivaldi, see if you have a lot of bookmarks and give snapshot build a chance.
I can't reproduce, I tried an .mp3 and a .torrent, the file is saved in the default download dir and the associated program is started.
Do you have any extension that could interfere? Can you try disabling all extensions and retry?
and disable it.
If there are any vivaldi.exe process active in memory, a new activation of vivaldi acts as if the user wants a new vivaldi window only, like ctrl-n, it is created but only with start page.
@c01313 Have you tried a fresh profile? (Your profile is the "Default" folder which, if you installed normally in Windows is in your user profile, appdata\local\vivaldi\User Data. If you re-name it, you will then be able to start with a fresh profile, and later recover any needed data from your old profile.