Social Networking Site Attached to My Blog?

I’ve been reading about multi-site and subdomains, and I’m having difficulty deciding what to do. Honestly, getting my head wrapped around it is proving a bit difficult. I think I’d have an easier time of it if I was pointed in the right direction, and then worked on the mechanics of that choice.

I have a blog, based on Atahualpa. It has a decent number of pages within it, making the menu bar a bit busy (2 rows). I want the ability to run a social networking site associated with the blog. BuddyPress doesn’t like Atahualpa, so I set up a Mingle plugin. It works, but it sits in a page on my site, and its menu is integrated within my blog’s menu, which makes it a pain for users to operate. After getting to this point, I decided it would be nice to have the SN site run in its own page, separate from Atahualpa.

I’m hosted on a shared server on HostGator.
Questions, and what I’d like advice on doing….

1) What do you think would be the best way to run a social networking site on a shared server, along side a related blog?

2) Do I need to set up a subdomain in order to run a separate instance of a theme, or in order to run a different theme altogether?

3) Does a subdomain require a separate install of WordPress?

Thanks. I’m sorry if this has been addressed already. I really did do some searching.