pohaver
That's about as many questions as I have seen in so little space! Wow.
First of all, "Yes, you can" to just everything you asked, IF you really want to. But you might not want to do some of it and probably won't as you look into it further.
Personally I like Dreamhost and use it altogether for my hosting. You get unlimited domain and subdomain hosting which leaves lots of options for any type sites. They give you incredible amounts of space to work with. Perhaps most important, they include support for just about anything (php, MySQL, WordPress, etc.) you could need to do anything. I never know what I will want to do next and wanted to avoid getting locked into a setup that didn't meet my needs later on. That's one of the main reasons I went with them. The last thing I want to do is move--my house, my ISP, or my host.
After getting your initial setup, it takes about ten seconds to add another domain, like
www.mywebsite.???, or a subdomain
www.blog.mywebsite.??? and you can have all you want at Dreamhost, some providers make you pay for each one so watch out.
Wordpress is very extensive. You can use it for setting up a site with almost any option imaginable. It doesn't matter what software you use in addition, most of us use a wide variety of them, you just upload the files you create with your ftp program (file transfer program like the excellent free FileZilla).
Good Success!
James