3. The kind of tab-switching that v12 had, right-click + mwheel and in last-used order,

This is unlikely to return. The functionality can, however, be recreated using extensions.

Not true as they don't work on internal pages (like the downloads page, or even way worse the new tab page). This is not even close to an alternative.

Right–click on a search field and choose Create Search Engine. Is this not what you meant?
That's it, but it's not working properly. I've set up http://startpage.com as a search, but when I try to use it, Opera Next just opens the page itself.

You most likely made an error. Use this how to: https://support.startpage.com/index.php?/Knowledgebase/Article/View/201/9/how-do-i-install-startpage-as-my-default-search-engine-in-chrome

This error is reproducible for me on Opera Dev 21.0.1419.0, http://www.zeit.de/wirtschaft/2014-03/Ukraine-Wirtschaft-Staatsbankrott on the right there is an embedded video, if I click to play that the video does not load. All I get is the red loading circle. Current stable of Chrome runs the video fine. Probably closely related to the Potlatch 2 error, that I posted here yesterday.

Please report your bug also to the Opera bugtracker. You can find it here: https://bugs.opera.com/wizarddesktop/

What are "proper" mouse gestures for you? Be more precise if you want features. Apart from rmb + wheel I am not missing anything mouse gesture wise. But I switched to Chrome since Opera 12 because of the render engine and the twitch.tv/flash bug when you switch tabs with the wheel. I reported the bug with all information and there was nothing they have done.

You can switch through the tabs (without preview) in last used order on your keyboard as soon as you activate opera://flags/#activation-order-tab-cycling . Maybe that makes Opera a little bit more usable.

Regardless of click to play or always load plugins the OSM editor Potlatch 2 will not run. For a brief moment you will see the inface after the loading screen finished then everything turns white.

https://www.openstreetmap.org/ after a login you can use the edit button.

edit: works on Chrome 33 just fine.