Did you try to disable sync on your old device? https://support.mozilla.org/en-US/kb/disable-firefox-sync

I cannot do this because I do not have this device anymore and the device is removed from my devices list.

Try to change your sync password https://support.mozilla.org/en-US/kb/disable-firefox-sync-lost-phone-or-tablet

OK, just did, let's see next hours or tomorrow. Thanks.

So, the same happens. Is it possible to contact support to delete all my bookmarks assigned to my account?

As a Firefox support volunteer I don't have the ability to modify something in others accounts and as I know no one can. By the way, at this thread the similar problem was discussed: https://support.mozilla.org/en-US/questions/1155190 And the solution was to wait 7 days after changing the password. Please bump this thread to let us know if it works in your case.

If you use Sync, best is to disconnect Sync temporarily during troubleshooting.

This could be a problem with the places.sqlite and favicons.sqlite files in the Firefox profile folder.

• use the "Places Database" -> "Verify Integrity" button on the "Help -> More Troubleshooting Information" (about:support) page

If errors are reported with "Verify Integrity", close and restart Firefox or reboot and retry.

If "Verify Integrity" cannot repair places.sqlite, rename/remove all places.sqlite and favicons.sqlite files in the Firefox profile folder with Firefox closed. Firefox will rebuild places.sqlite and restore the bookmarks from the most recent JSON backup in the bookmarkbackups folder.

• keep a backup copy of places.sqlite in case a new places.sqlite database has to be created
• you lose the history when a new places.sqlite is created

You may have to restore an older bookmarks backup in the bookmarkbackups folder via the Bookmarks Manager (Library).

• Bookmarks -> Manage Bookmarks -> Import & Backup -> Restore
• https://support.mozilla.org/en-US/kb/restore-bookmarks-from-backup-or-move-them

See also:

• https://support.mozilla.org/en-US/kb/fix-bookmarks-and-history-will-not-be-functional
• https://support.mozilla.org/en-US/kb/cant-add-change-or-save-bookmarks

You can use the button on the "Help -> More Troubleshooting Information" (about:support) page to go to the current Firefox profile folder or use the about:profiles page (Root directory).

• Help -> More Troubleshooting Information -> Profile Folder/Directory:
  Windows: Open Folder; Linux: Open Directory; Mac: Show in Finder
• https://support.mozilla.org/en-US/kb/profiles-where-firefox-stores-user-data

@Alex R - looks like password change and constant deletion of additional bookmarks helped :) Thank you