See below for answers to your questions:
Now, I need some help from you guys! Which operating system should I choose (Ubuntu Server, or something like that. For the time being, I want a free operating system). How can I install/configure the operating system and how to get it up and running? How can I install Joomla 1.5 on it (it needs MySQL)?
I would say look at Ubuntu Server with a LAMP (Linux, Apache, MySQL, PHP) install and then install Joomla on top of that.
And how can I install/configure email accounts for my domain?
Check out Zentyal (used to be called ebox)
I’ve also heard of a software called Webmin. What is this?
Webmin is a web-based interface for system administration of a Unix / Linux Server.
Is there any other software that I can use for managing my domains, files, email accounts, etc. (something like Parallels, or cPanel just that it needs to be free or really cheap, because I’m currently on a tight budget)
As I mentioned above check out Zentyal.... It's free :).