PinkElephant

OK, desktop challenge. This is on my MacBook Pro, BigSur 11.6, Safari browser ver. 15.
Works, and by seeing the blue + sign it is even easier to follow what is going on. The + shows by itself when moving the mouse pointer over it.
My conclusion: I don't know what technology EN uses to build the animated web client. But maybe something on your Linux desktop or in Chrome (maybe a popup blocker, or similar) is blocking it. So it seems to me this is more an issue for support than for the forum (which is user2user).
 

Tables WebClient.mp4  
 

Tried this already ?
Go to the Evernote menu, Preferences, and uncheck „Keep data when leaving“ Log out of EN (File menu), quit EN (cmd-q) If you want to be very sure, restart the Mac Open EN, log back in, wait for it to run an initial sync.  All steps are important, don‘t skip any.

On the mobile clients, only 1 note can be selected at any time.
As a workaround, on tablets you can use the web client. It allows multiple selections. On a phone it is difficult to use.

From the syntax I think it should be spelled
-notebook:“neuralnetworks perceptron“

@Job135 Maybe there is a mistake in the local copy of your data. You could try this:
Go to File > Sign Out [name] from the menu bar. Select the "Remove my Evernote data from this device" option, then click Sign out. Restart your computer. Sign back in to Evernote

Oooops !
Probably somehow (don’t ask me how) EN was set as new standard app for all of these file types.
You can reassign another standard app (like Adobe Acrobat to pdf or Word to doc) to one of the extensions, and see if it returns to its normal look. If it works for one, you can do the same for the others.

Just a little improvement: Don‘t use the feedback, issue a support ticket.
AFAIK to a feedback no activity log can be attached, and there is no answering by EN on feedback.
You find both options in the app settings, tab support.

This is how stacks and notebooks should look when you select „Notebooks“ in the left panel. The first stack is open, the carret points up to collapse it, the second is closed, the carret pointing down to expand it.

It seems you have done most things right in securing your account. However when reading to me it is not entirely clear what you have done to secure your account:
You say you sign in with Google. Fine, but when you created your account, it most likely was done by an e-mail address and a password.
THIS is the password that probably is used to access your account, not your Google login.
No matter how it got exposed (usually by being a weak password, or a reused one), you should change THIS password ASAP. Because when you get the 2-FA note, it means that somebody used the correct UserID and password, and is only one step away from getting access. Better make this attempt a futile one by resetting the password.
The other stuff like a Passcode and FaceID only help with the local security of the app, not with the remote access that causes the messages to pop up.

Not sure what is behind this message.
If you made your „clean my inbox“ day, it may be you exceeded the daily mail limit. You can send up to 200 mails per day into one EN account.
If you went beyond it, wait for the next day until it resets. I am not aware you can check this in any place.

If you can’t enter the app, you need to do a FULL uninstall.
Get yourself an uninstaller app - for Windows Revo Uninstaller has a good track record.
Make sure all program parts including the data folders (!) are selected, then uninstall.

If you properly used AppCleaner, there is NO data left on your Mac.
After you opened AppCleaner and dropped the legacy icon on the field for removal, a window opens. It lists all components of a program, including the data files. By default data files are not yet checked.
Now check ALL  checkboxes for removal - then scroll the window down and check more, until you have checked them ALL.
This will remove program, settings and data. After a restart you get a fresh install.

You could try this: Go to the Evernote menu, Preferences, and uncheck „Keep data when leaving“ Log out of EN (File menu), quit EN (cmd-q) If you want to be very sure, restart the Mac Open EN, log back in, wait for it to run an initial sync. If this doesn’t work, uninstall using the app AppCleaner, restart the Mac and install fresh from the EN website.

There is note history running on every account in EN. Access is a subscribers feature.
Through note history older versions of a note can be reviewed and restored. Either they replace the current version, or you save an older version as a new copy. It is found in the note information menu.
If the content is not found in note history, you need to contact support.

@david_woznyorg Even if you accidentally delete a notebook, all content (not the notebook itself) goes to the trash. You can create a new notebook, select the notes from the deleted one in the trash and move them into the new notebook.
Just don’t empty the trash !

It was impossible for me to reproduce ANY of your claims. All of your problems do not describe the function of the actual web client.
Any chance you have rested your web client to the "classic" editor by accident ?
Overview - EN web - new version must be active Personal settings - web client - v10+ must be active

You use the search syntax, open for all accounts.
https://help.evernote.com/hc/en-us/articles/208313828-How-to-use-Evernote-s-advanced-search-syntax Examples (type what is in between the <  > )
<cat dog> is equal to     cat AND dog
<any: cat dog> is equal to     cat OR dog
<cat -dog> is equal to      cat NOT dog 
This is EN standard and exists since a very long time. It even got better now with the CONTAINS command.
When you hit Enter, it works as an interpreter, reading and executing the term left to right. It is possible to build longer expressions, but not very complex ones:
<stack:personal tag:2019 contains:fileimage any: cat dog>
will find any note with cat or dog (or both), containing an image file, tagged with „2019“ in any notebook in the Personal stack.

We are talking about the Mac desktop app, not the iOS app here. I assume you are a subscriber, since you mention a support ticket.
Can you get to the apps menus ? If yes, this may work:
Go to the Evernote menu, Preferences, and uncheck „Keep data when leaving“ Lag out of EN (File menu), quit EN (cmd-q) If you want to be very sure, restart the Mac Open EN, log back in, wait for it to run an initial sync.  If no, you need to make a full uninstall. This means to get the app AppCleaner and use it to remove every part of the program and data. After that, restart the Mac und download a fresh EN copy from the EN website.

OK, understood. If it is only the active part that stays on, probably no syncing problem.
About your other ideas it would probably be better to send it to EN using the feedback function.

Sorry for a misleading initial answer. Just moved my body from the couch to my desk, and had a look on my Mac: If you click into the search field (left panel, top), a dropdown menu opens.
Below the field for the search string, there are the last searches, and then a block for saved searches. They have a down arrow to see them all, if the overview is too narrow for a complete list.

If you are on a subscription, you can access support about it.
If you want to downgrade, it depends on your method of payment. Simply withdraw the medium of payment (like a credit card), and let the subscription expire. Your account will automatically be downgraded to Free after a little while (Icgot a week for free to think it over).

v10 is tag by tag. But because often you will want to replace old, to be deleted tags by new ones (for example out of the reasons I have listed above), you anyhow need to move tag by tag.
Decide about a tag, then select all notes containing it, then assign the new tag to all of these notes, then delete the old tag.
You can't do this for several tags at once, or better you can, but you risk deleting tags before the new selection sticks.
In general if you want to clean up a lot, I would install the legacy client, since it supports such an action better than v10.
 

If it is plain text: Select ALL in both notes and copy each to a text file, like MS Word or a free competitor as LibreOffice or OpenOffice.
They have tools to compare 2 text files and mark all differences.
Decide about what to keep, select all in the resulting text file and copy it back to EN.
To avoid many conflicts keep your notes short. Split long notes into several smaller ones. Create a TOC note and insert links from one note to another to make navigation easier.

@Caio Alvares You are on the Free plan now.
You probably exceed your device limit. Go to your account, devices and unsync devices to get into the limit of 2.
The web client counts as a device.
https://help.evernote.com/hc/en-us/articles/218558068-Understanding-the-device-limit

Did you ever have a beta installed ?
Then check this:
https://help.evernote.com/hc/en-us/articles/360033369173