You say "my own domain": I assume you have bought a domain AND are renting a server for that domain, something like "www.mydomain.com" and NOT "mydomain.godaddy.com" (which is a SUB-domain of godaddy.com).
In this case, and if you have php and mysql, the answer is yes to both questions, BUT you will have some work to do!
Make sure you have your own "site" set-up, with a home page visible at www.mydomain.com. That's the first step.
If not, you have to create your website first.
Once created, you can add more features.
To allow some people with usernames and passwords, you need to set-up a login system.
To create a message board, you have to write a script.
You can download "miniblog" and "login" scripts from http://www.web2coders.com. They are free.
Download as well Notepad++ to edit these scripts.
Both use Php and Mysql.
Good luck.