The value of having them on the same server under a single reseller account is objective, but I'd say it's worth it.
They staff should migrate the sites for you if you'd like them to and I believe they do that at no cost. They'll carry over all over your current settings into your reseller account. Each account will have a separate cPanel account just like they do now, but you'll also get a single Web Host Manager account to create, modify, and delete your cPanel accounts. Adding a new account at that point is simple and does not require contacting TCH to do.
The server settings will be the same. You would have to change the DNS servers at your registrar, I believe.
As far as billing, yes, your 3 separate payments would be terminated and you'd only be billed for the reseller account.
No problem. Hope my answers help!