Yes your email account from freeserve will be closed and a new email address will be provided by your new supplier.
I'm a bit rusty but is FS anytime dial up? If so you can run your accounts concurrently as Broadband will take a little while to set up, varys with ISP but anything from 5 - 10 days. Braodband and Dial up can coexist so you won't lose your internet connection for a few days.
As for cancellation, check your contract or contact Wannadoo (what Freeserve has become) to see what notice you have to give.
If you want a more permanent email address you could always buy a domain name, .uk ones are very cheep at the moment, but you do have to pay a extra for your ISP to host it.