You should be able to access your control panel as soon as you get your welcome e-mail, it will have instructions on how to do so.
As for e-mail, I'm not sure. DNS propogation (swiching the domain name to TCH's servers) can take anywhere between 24 and 72 hours.
I'm no expert, but I think that all e-mail sent to you, as long as you have the same account name on the TCH servers, will be caught by either your current server or TCH's, depending on whether the domain has propogated or not.