Is WordPress compatible with HostGator

What exactly is WordPress?

These are some very basic questions, so I apologize for asking them, but it's hard to understand exactly how some things work without experimenting with them for dozens of hours. I am more than willing to learn WP if it can do these things, but I only need a few Yes / No / short explanations Answers to know what WP can do.

  1. I know WP is some kind of blogging system, but can I use it to blog posts on my own domain?
  2. If so, can only the web administrator create it, or can anyone on the website create it?
  3. If WP can blog on my own domain, do you just have to throw some server side script files in a directory on my site and then do the blog posts in my browser?
  4. If so, will it manage blog accounts by itself, or do I need to create an account / login / password / etc system?
  5. If WP can create a blog system in my domain that all users can use, the CPU usage WP is causing will end up costing me $ 100 / month with only about 20 active bloggers on my website, or are the CPU utilization calculations caused by WP insignificant?
  6. Does WP have a forum-like functionality or is it only about blog posts + comments + Facebook "Likes" / Digg Votes / etc.?
  7. Does the host of my website (HostGator) have to support WP in any way (regardless of whether they are server-side files that I cannot store on the server myself, except for PHP? And MySQL, which HG offers), or whether it does is some site hosts not allowing WP etc to be used? I know HostGator doesn't allow warez, music sites, games, etc. Websites but they shouldn't have a problem using WP right?

As I said, if it sounds like what I'm looking for, I'm more than happy to buckle up and learn. I just need to know what WP "is." I apologize again for my deep ignorance.