The forum can either be a support to your website / blog or it can be standalone. The choice is entirely up to you.
You will be required a web-host and a domain before proceeding with this gig.
If you don't have either of them, I will set you up with a free web-host and domain.
Yes, you will need to have your own domain and hosting account. I will just install forum on your host.
On your special request, I will create you a forum based on free domain and host by myself with no extra charges.