Menu -> Mail accounts -> select the account -> edit -> switch to Outgoing tab -> Edit Signature".
If you're going to create an HTML signature and you want to add a picture to it with <img src="">, don't add the img tag in the signature editor or it'll crash Opera Mail. Instead, goto "Menu -> help -> About Opera Mail" and take note of the mail directory location. Then, close Opera Mail and edit the signatureN.txt file in the mail folder where N is the number for the account as seen in accounts.ini. Doing things that way will avoid the crash. If you're not inserting an image, no need to do all of that.
I am still puzzled about why only Opera (my 12.x version, Opera Mail and standalone) duplicate sent messages, whereas Outlook and smartphone app do not. And why all this started a few weeks ago...
Maybe something changed on the server where the server is no longer ignoring Opera's duplicate and it still ignores other clients' duplicates. And or, maybe some other clients don't add a copy of the sent message if it's an exchange server. I'm not sure. I would guess that for Outlook, it's probably not using IMAP to connect and is using the actual exchange protocols etc. For the smartphone app, I guess maybe look in the settings. It may reveal something.
I'm pretty sure Exchange has been creating its own sent copies for a while, so I doubt that was off and hotmail all of sudden turned it on.
Close down Opera Mail and edit operaprefs.ini. See "Menu -> Help -> About Opera Mail" for the location. Under [User Prefs], make sure "Show Notification For New Messages" is NOT there so that Opera uses the default for the setting (which is 1). You can keep it there and set it to 1 if you want, but do the other way instead. Then, make sure you never mess with the checkbox in the settings UI as it's broken. It's really only broken for unchecking (trying to set it to 0), but just avoid the checkbox for good measure.
That's probably not going to help as you already get notifications sometimes. But, I'd try it just for good measure so that you know the setting is right.
Then, while Opera Mail is closed, for each account in question, check the section for the account in accounts.ini in the mail folder. You want Sound Enabled=1 set and Sound File=path to .wav file (make sure it's a .wav file).
That's probably not going to help either as it sounds like things are set correctly.
Then in the UI under the settings for each account, on the Incoming tab, make sure "Include this account when checking manually" is checked. Make sure "check every..." is checked and set it to less than 30 minutes (and no less than 10 if the server has a problem with you checking too frequently). You need to do that even if you're using IMAP and IDLE so the IDLE connection doesn't time out. You also need to make sure you're not using low-bandwidth mode.
If everything's good and you still have the issue, you're out of luck. It just happens for some people in Opera Mail and no one has ever figured out why.
While Opera is closed, you can add/set Show Attachments Inline=1 under [User Prefs] in operaprefs.ini (see Menu -> Help -> About Opera Mail" for the location).
Just note that option isn't just for printing, it's for viewing too. This means, you'll see the attachment filename in the body when just reading. Also, you might not always see the filename and whether you do or not, the actual content of the attachment might display in the body depending on the type. But, it's something you can try.
Besides that, I'm not sure. You might be able to add something in mime.css in the styles folder in the program files folder. There's an @media print block in there. But, I don't know if that'll help.