I'm assuming you've setup qmail to deliver to Maildir type mailboxes... if you haven't then some of this will not help. (Maildirs are pretty good though.)
A1: receiving mail. have a look for mutt or pinq or other command-line progs that can read a Maildir.
A quick&dirty thing to do with a Maildir is look for new files in ~USER/Maildir/new directory. Any file there is a message the user has received and not read yet. If USER doesn't have a Maildir then it won't be delivered - messages will stay in the queue and eventually bounce.
Port 110: did you set up a POP3 daemon? if not, that's what you need to allow clients on other machines to get mail. (Yes, there are other things than POP but he said port 110, ok?) qmail-popd is the obvious choice if you're using qmail. The FAQ with qmail tells how to do it, you also need to build checkpassword from
http://cr.yp.to
A2: Set the clients to use 192.168.0.X as the SMTP and POP server.
Username: The standard thing is to make a Unix user account for each user and make a Maildir in their home directory. They don't need to have shell access, the POP server will check their Unix username and password and let them have any mail that's waiting.
A3: I don't use mutt but if your'e running it on the mailserver, you just have to tell it to read from your Maildir. If you're running it on a different machine, you still have to get the mail to that machine before you read it with mutt - a unix host can run its own copy of qmail, or you setup fetchmail... (Or not, I use a nice GTK mailreader called sylpheed which does POP and SMTP. Highly recommended.)
If it's going to have an internet connection, please check your new mailserver isn't an open relay! The spammers WILL find it.
Some links:
http://www.qmail.org - has all kinds of info.
http://lifewithqmail.org - an alternative, worth dipping into.
http://sylpheed.good-day.net/ - sylpheed mail client