I had to go through 4 or 5 tutorials myself before i got one right, i just finished "the perfect server" tutorial by falko, by the way mad props to him he's knows his stuff. I ran into many many problems and i'll do my best to offer any assistance i can. Let me clarify a few things, you cant login to outlook or thunderbird, or squirrelmail? but the "basic" method from the console on the server lets you send? show your postfix config so we can look it over for errors, might help diagnose the problem. its located at /etc/postfix/main.cf , also when you try to login via outlook or thunderbird what error does it give, the whole message not just the error code, and do you get past the password authentication? Also try going into account options and checking my server requires authentication, also i noticed this in your logs Jan 11 00:34:01 exampleserver authdaemond: authmysql: MYSQL_SERVER nor MYSQL_SOCKET set in/etc/courier/authmysqlrc.
Did you follow that part in the tutorial right, go and double check all the parts where you do mysql commands. I found out while doing mine that mysql does not accept passwords that have special characters in them, so make sure you dont, hope this helps some.