The Oracle Java plug-in should be working in Opera developer and Opera next within the next week or two. Which means it should work in Opera within the next six weeks or so.
What type of account? For POP3 accounts it does by default; for IMAP it downloads only the headers until you select a message to read - but defaults can be changed. You can set it as to whether or not it retains the body of the message when you shut it down (so it doesn't have to fetch them again if you want to reread them - or so you can reread them even if you're not connected to a network) and as to whether it fetches only headers or the full message, and so on - when you go to account properties there are a variety of options on the "Incoming" tab.
There is a flag in opera://flags/#find-pepper-flash-plugin (if you want to test out the Pepper Flash (maybe unstable))
Try right clicking on the flash content and see if the quality is set to High, for videos, check the video player for an option to choose a Higher resolution video (can take more time to load)
I assumed that I could use the same combo as for Firefox fullscreen mode (which is command-shift-f).
Now I know better!
No, it is aligned with Safari (as it is the system default). Sorry about the confusion! You can see shortcuts by exploring the menu bar or see them all listed in Opera Help (from the Help menu).
Flash is not forced for me. My setting on https://www.youtube.com/html5 is respected, even when there is no VP9-video and all Opera can play is the VP8-fallback at 640×360.
And yes, I have Flash Player (15.0.0.152) and it is enabled, and used on YouTube if I choose to use the default player.
For my IMAP accounts, I just leave everything in the Inbox and use Opera's labels and Opear's All Messages views to filter what I see in the Inbox IMAP folder. It's kind of like custom views in Thunderbird.
Keynote, Numbers, and Pages documents are really folders. Opera Mail isn’t quite smart enough to figure that out. You can zip/compress/archie the documents in Finder before sending them.
ISPs are supposed to block port 25. If you were using port 25 and they didn't block it till recently, that could be the reason. Or, your mail provider could have finally disabled port 25. If you were using 587, not sure why that'd quit working on you.