I'm having this problem at the moment. If I go to the linked anandtech article and right click -> save image Opera offers to save as jpg (at least the few I tried). So different as for the OP.
If I go to https://ae01.alicdn.com/kf/HTB1fHwISpXXXXXQaXXXq6xXFXXXQ/NEW-Original-Remote-Control-for-GRUNDIG-3D-TV-Remote-TP7187R-3-Fernbedienung.jpg and try to townload or drag and drop the image it turns into a webp. Even though the url says jpg.
This behaviour doesn't change no matter what I select in the user agent switcher (this one)

So, just in case someone else has similar problems and finds this via google, here's the solution to this particular one:
Flash was somehow corrupted. After I reinstalled that, everything is back to normal.
Including still broken audio.

I tried restoring various things from time machine. I'm now at a state, where it tries to load the last session with all the windows and tabs. It even loads some of the pages and then crashes. After one or two more tries it doesn't try to load that session but instead opens one window and then crashes. Trying to open Opera again opens just that window, crashes, tries again, crashes and gives up. I would imagine that if a page causes the crashes it wouldn't be a problem once it goes to one page but maybe it is?

Is there a way to find out which page may have caused a crash? If it is that problem.
Is there a way to start Opera clean? Maybe a terminal command?

It would also help if someone other than me answers.
Is there a way to tell the Opera staff perhaps? Do they care?

The last bit was supposed to mean "Why and when it works or doesn't I don't know. Also no idea how to fix it."
I'm so good at typing...

Perhaps some additional info.
These problems started today after I had some unrelated problems where Finder would crash loop, because I had some files that Finder didn't like. I think. After removing them in Safe mode, the Mac started properly and I can use the system now. I suspect that some opera file got corrupted while Finder was spazzing out, but I don't know what other files could be the cause.

Also, I looked into Console and found in a crash report:
abort() called
/SourceCache/libpthread/libpthread-105.40.1/src/pthread_mutex.c:pthread_mutex_unlock:776: __p_mutexdrop failed with error 22
with lots of stuff before and after. Googling that just gave me a crash log from someone else without any explanation.

Also, I'm on 10.10.5 if that helps.

As the title says, Opera wont start. It very briefly shows a blank page where it says something like recoverd from crash. I think. Opera closes too quickly to read it.

I reinstalled Opera both in its newest version and in version 31. Same problem.
I tried a clean restart, so I moved home->Library->Application Support->com.operasoftware.Opera elsewhere.
Same with home->Library->Application Support->Opera (i don't know which of these is for modern opera?
I removed the folder home->Library->Caches->com.operasoftware.Opera

Is there some stuff elsewhere?
(I googled for opera config files or something like that. I found this: http://www.opera.com/docs/operafiles/
Is this for modern Opera? It references Opera 10 and 12. In any case, I moved those files as well, if I found them.)

Yes I have that issue (except the volume one).
Oddly enough, it sometimes works. As in, I switch on my bluetooth headphones, they show up in the list and I can switch to them.
But often it prevents them from showing up. Or they show up but switching to them does nothing.
Those problems are then fixed by either closing Opera or doing "sudo killall coreaudiod" in the terminal. Which is annoying.

Why and why it works or doesn't I don't know. Also no idea how to fix it.