Switching to WordPress with a Pre-existing Website

Hello!

I am running a non-profit website which is old and outdated. It is already hosted by a local host. However, I want to not only change the host, but also convert the website, which is a .org URL, into WordPress. Here are my questions:

1) Can I use a host that is not listed on your suggested host sites, like a local one in my town?

2) Will I be able to keep the same domain name/URL of .org status if I change to WordPress?

3) How do I begin to do that?

4) What is the cost of operating a WordPress.org website per month or year?

Help!

Thank you so much, I could use all the help I can get.

Kellie