Is it just me, or is there no 'server' in 'library'? Spotlight can't even find it. What now?

The local user's ~/Library folder has been hidden in recent releases. It's still around, but it's been added to the list of stuff that doesn't show up (by default) in Finder. The system-wide /Library folder remains hidden.

As for your question, I'm not certain what you're working with here, and some details could help me understand that. (Part of my confusion: this is an OS X Server operating system forum, and it's not common to encounter the Snow Leopard Server OS X Server 10.6 software loaded on a MacBook. There is a Server folder involved with that package; that's where the management tools are stored on an OS X Server configuration, and also when the server tools package is installed on OS X client. There's also a mail server involved.)

I'm going to guess that this isn't Mountain Lion Server OS X Server 10.8, though...

What steps are you looking at, and that don't match what you're (not) seeing?

What application(s) are involved?

What version of the application(s)?

Your footer shows Outlook.com; if this is a mail-related question, is that your mail server here?

OS X Server is different from OS X client. If you want to run a mail server (which also generally requires static IP and public DNS), then acquiring that package is the easiest way to deal with this. And you'll probably be working with Postfix settings and related.

However, it appears you're possibly tangling SMTP server-side settings, OS X Server settings, and Mail.app mail client settings together. The reject_non_fqdn_helo_hostname setting only works on a Postfix mail server, for instance. This and other Postfix settings are server settings. These settings are unrelated to Hotmail, Gmail and Outlook.com; the administrators of those mail servers will have configured the server-side settings as they need, and it's up to you to configure the mail client settings.

Here are the mail client settings for Outlook.com. The set-up and ports look fairly typical of most any recent mail server set-up; The send path SMTP TCP port 587 with SSL/TLS enabled, and the IMAP receive path is TCP 993 with SSL/TLS. Not sure why you're having issues, but the Mail.app Connection Doctor tool (Mail.app > Window > Connection Doctor) might help locate the trigger.

Mail uses two paths.

One for retrieving messages from the server, and another for sending messages.

The host server Mail.app (or whatever client) you're receiving your mail from doesn't have to be the same host as the server you're sending, too.

SMTP or a variant is used for sending mail from your client to your mail server, and from there to the recipient. This means you specify the hosts and ports as documented by the provider, and whether SSL/TLS is enabled or disabled.

The two protocols commonly used for receiving mail from a server are POP, and IMAP. (Given the choice, I'd almost always use IMAP.) This means you specify whether you're using POP or IMAP, the host name you're receiving your mail from, and whether SSL/TLS is in use.

In the case of Outlook.com, you need to log in (via the web mail interface) to see which server(s) you need to specify for sending (SMTP) and for receiving (POP or IMAP) mail. You'll then use these servers in your set-up.

Check your settings for the receive path. POP or (preferably) IMAP, with the right host, with the right port, with SSL/TLS enabled or disabled.