Currently, yes. Basecamp Personal is offered exclusively to existing Basecamp users. You don't have to be the owner of a Basecamp account - you only have to be a user on a Basecamp account. We plan to open Basecamp Personal up to the wider public in a few months.
Nope - Basecamp projects and Basecamp Personal projects are entirely separate. No one from work will have access to your Basecamp Personal project unless you expressly invite them.
Nope - your Basecamp Personal project is yours no matter where you work. You paid for it, you own it. It's entirely separate from your Basecamp account at work.
That's correct - there is no monthly fee to use Basecamp Personal. You pay just $25 per project, one time. Once you buy a project you'll never have to pay for that project again. If you want to start up another Basecamp Personal project, it'll just be another $25, one-time.
Basecamp Personal projects include 1 GB of space to store files. We plan on offering the option to purchase additional space down the road.
You can work with up to five people on a Basecamp Personal project.