Well yeah, pretty much every forum out there relies on MySQL to store data. So yes, you need MySQL databases to run a forum. If anything, all you have to do is go into cPanel, go to MySQL databases, and tell it to create a database with a name of your picking. After, you can upload your choosen forum software such as SMF or phpBB, and enter in the information like your server's MySQL settings, like Localhost for the database server, and your MySQL username and password (your cPanel name and password if you didn't set up a MySQL user and pass), and your database name (as shown in cPanel). After, you're good to go.
Or, if you want to save the hassle of doing all of this, Fantastico, after you pick what software you want to install, will create the database for you and will install everything (even put the files on your account) for you or at least guide you though it. It may not have the latest version of the software, but it is a convenience offered here, and of course you can always upgrade the software manually from the maker's website, which is recommended.
As for PHP, just make sure that at
http://www.x10hosting.com/account you have requested Intermediate PHP and you're all set to go! As for keeping your account alive, all you need to do is log into the forums briefly before the two week period expires, and you're good to go for another 2 weeks. You don't need to post a thing, but you can post if you'd like, and I'm sure you will. Besides, posting after a while not only allows you to enjoy what x10 can offer, but you can learn some new things here, have fun with other people, and see the credits below my post count? Whenever you post, you get credits, which can go towards things such as money via PayPal, and even a free domain name of your choice for one year.
As for that inactivity suspension, if you haven't done so already, request an Unsuspension in the Free Hosting forum and the staff will take care of you
.
Hope I helped.