2. I have a nice broad monitor - I want to move the search tabs from the top of the screen to the side - as well as any menus;

Opera can't do this. But, Vivaldi has some things you can do in this area. For example, you can put the tab bar on the left of the screen and enable/disable tab thumbnails.

3. I want to be able to sync tabs and search history to a local pc - not to the cloud.

Do you mean you want to have your own sync server running on one of your computers and set up Opera Sync to use that server as the sync server instead of Opera's? If so, I don't think you can do that.

If you're just talking about storing those things on your hard drive, Opera stores those things by default in the profile directly. You don't have to do anything to make this work. But, you can use the Session Buddy extension to further manage your opened tabs and save them. You can also right-click a tab and choose to save all open tabs to a speed dial folder where you can then right-click the folder and choose to open all of the pages in it.

1. I want the bookmarks, search history, etc to be stored on and USED FROM a thumb drive (not just backed up to);

When you launch the installer, click "options", set the "install path" to a folder on the thumb drive, set "install for" to "standalone installation", adjust other checkboxes and install. Then, Opera and all its profile data will be on the thumb drive.

If you want Opera's program fiels to still be on your computer and just Opera's profile data on the thumb drive, you can modify Opera's shortcut to launcher.exe to pass the --user-data-dir switch to it.

Example:

"C:\Program Files\Opera\launcher.exe" "--user-data-dir=k:\Opera Data"

There's also --disk-cache-dir. But, you'll have to make sure Opera isn't launched by file association and is only launched directly or those command-line parameters won't be passed (unless you used some browser launch utility that allows you to set it as the default where it passes to launcher.exe with the switches you want).