The problem seems to be solved.
I have downloaded a "new installation" of Opera Mail and with it the outlook.com and hotmail.it accounts work. Moreover now, the "original installation" of Opera Mail also works.

It seems that the "new installation" unlocked something and now everything works.

Now, looking at the log file appears again the message:
06/07-2015 14:31:52 IMAP#1/1: Disconnected: Connection closed by server, unexpected disconnect

But now, after some seconds (3 minutes maximum), it is followed by:
06/07-2015 14:31:57 IMAP#1/1: Connecting...

This last automatic re-connection has always successful.

What I continue to not understand is the frequency. These automatic operations are done about every 2 minutes, but I have set a synchronization every 10 minutes.

However all seems to work fine. I have monitored it for 2 days. I will continue to monitor it for the next days. If the problem will appear again in the future, I will continue with this discussion on the forum.

Thanks very much to burnout426!!! I really appreciated his very precise help!!!
The solution comes from him, thank you again!!!

First of all, thank you very much burnout426 for your very complete answer!!!

I have set to synchronize every 10 minutes these accounts.

Just to double check, you have 10 set in the text field for the setting, but do you have the checkbox for"check for new messages every..." checked? (I assume so, but asking just in case)

Yes, it is checked.

Does the log show that Opera is indeed checking every ten minutes. Do you see IDLE in the log?

I don't understand very well what you mean, however there isn't the word IDLE in the log.

Are you using imap-mail.outlook.com (port 993 with TLS checked) and smtp-mail.outlookc.om (port 587 with TLS checked)? There are (or were at least) some older live/hotmail IMAP server addresses that may be running an older IMAP server that you might want to avoid.

The parameters of the server are exactly those indicated by you. However the hotmail.it account is very old (about 5-6 years), while outlook.com account is new (about 2 weeks). Both are configurated as indicated by you.

Any anti-virus with an email scanner?

No. I have a classic Avira Free antivirus (the Mail Protection is not included).

Try double-checking in Thunderbird to make sure it's not messing up there too. Create a new outlook.com account just to test with and test that in Opera to make sure it's not just something with your account (sometimes can be).
Download the Opera Mail installer, launch it, click "options", set "install path" to a folder on your desktop, set "install for" to "Standalone Installation (USB)" and install. Set up the IMAP accounts in it (do not import) and see how things work fine there. If they work fine there, you should just be able rename your "mail" folder for your regular Opera (while it's closed of course), start Opera back up and add the IMAP accounts back in.

I use already a portable version of Opera Mail. However I will try to use a "new" Opera Mail with those accounts and a Thunderbird checking.

Is the time, date, time zone and daylight savings time settings on your OS correct? That can mess with secure connections if they're not correct.

Yes, it is all correct.

You might want to look at the log before the disconnect the server does to see what was happening before. In some rare cases, a single message in a folder can cause problems. But, usually you'll see the log stop at that point.

Mmmmhhh, I don't think so because my outlook.com account is new. There is only one mail in it: the classic welcome mail by Microsoft.

The force single connection option was necessary in the past for hotmail. I don't know if it's needed now with the outlook.com IMAP servers.

Nice, I understand. Thank you for clarification.

Thank you again for you help burnout426!!!

Hi to everyone!!!
I have problems using the two accounts specified in the title.
I have set to synchronize every 10 minutes these accounts.

When I start Opera Mail they work fine, but after about 30 minutes a yellow hazard symbol appear near them and they stop to work. In some cases they start to work again after some hours.
I have done some "experiments": I send them a mail with a Gmail account. In some cases they receive correctly the mail, but in other cases they receive the mail after 1-2 hours (it happens when I send them the mail and the yellow hazard symbol is at the same time displayed).

I tried to use log function (http://www.reddit.com/r/operabrowser/wiki/m2tips/enable_logging) and the error that cause the stop in synchronization is:
02/07-2015 12:12:19 IMAP#1/1: Disconnected: Connection closed by server, unexpected disconnect

I tried to apply the correction: Disable QRESYNC=1 and Force Single Connection=1
as specified in this post: http://forums.opera.com/topic/6539/re-opera-mail-imap-for-outlook-server-yes-or-no-cuz-ive-got-issues-receiving-sending
But nothing happens. The problem is not solved by it.

I read here in the forum and in web that is not an unusual problem with Microsoft accounts and Opera Mail, but how to fix it definitively? I am rather tired of this error because I can not rely on Outlook and Hotmail accounts.

I hope someone can suggest me something...
Thanks in advance and sorry about the long post!!!

Ok, thanks for your reply... I know the possibility to personalize the "Reply=" line and to insert "\n" to add more blank lines. I hoped that you could personalize also the automatic blank line (maybe modifying another text files similar to accounts.ini).

Thank you again!! Have a nice day!!!

Hi to everyone!!!
I have a particular request about Opera Mail.
By default, when you reply to a email, Opera creates a reply similar to:

1. First line: "On date 01-05-2015, Name Surname wrote:".
2. Second line: BLANK LINE.
3. Third and next lines: quoted original message received.

I would like to remove the BLANK LINE between 1) and 3)!!!

I have searched a lot on internet and in Opera Mail configuration text files, but I don't find a solution.
I hope that someone can indicate me how modify it!!!
Thanks!!! Have a nice day!!!