There are a lot of questions in there, maybe enough for three other SF questions.
why Outlook on some Win7 installations works but not on others,
Because there is a (important) difference.
Maybe the User/Password combination (check you mailserver's logs), maybe the good old KB3067639 ("Update to enable TLS 1.1 and TLS 1.2 as default"), maybe the keystore (and something is suddenly untrusted?), maybe other stuff. There are thousands of possible errors and it's nearly impossible to debug that without more information. Like Version/s, Patches, Logs and so on.
It would be helpful here, to see what your mail server says. Is, for example, the crypto failing, or the authentication itself?
and what Thunderbird does differently.
A lot of things.
Under the hood both clients are speaking (somewhat) SMTP, but the implementation of that is very different. Additionally, you are using TLS - Outlook uses the windows crypto API (CryptoAPI or CNG), Thunderbird bring it's own (more or less plattform independent) API and certificate store. Which is, sometimes, a pain in the ass when you try to distruibute certificates in a corporate environment. But thats another story.
I believe the mailserver is Dovecot.
Check those logs. And/or check your outlook logs.
Microsoft Outlook supports the logging of all communications that occur between Outlook and your email servers. Outlook can log the communications among Microsoft Exchange, Post Office Protocol version 3 (POP3), Simple Mail Transport Protocol (SMTP), Internet Messaging Access Protocol (IMAP), and Outlook.com.
How to enable logging
To enable logging for Outlook and Outlook with Outlook Connector (v14+) in Outlook 2010 (last supported one), configure the following registry key(s):
HKEY_CURRENT_USER\Software\Microsoft\Office\14.0\Outlook\Options\Mail
EnableLogging 1
HKEY_CURRENT_USER\Software\Microsoft\Microsoft Office Outlook Connector
DWORD: TracingLevel
Value: 3
How to disable logging
To disable logging, simply set them to back to 0.
Where are the logfiles
The POP3, SMTP, and MAPI transport types are written to a single log file in %temp%\Outlook Logging\Opmlog.log
.
I am quite sure, that will point you in the right direction.