I am not sure at 100% what are you asking about so I'll describe our domain name policy in total.
We are not doman name registrar and we host domains that are already registered with some 3rd-party registrar. So if your domain is registered then all you need to point it to our server is to put our nameservers in to your registrar's account as primary and secondary nameservers for your domain. In this case the domain starts to work drom our server in 1-2 days after the new DNS zone will be fully propagated.
But it looks like you want to leave your current registrar. So we can transfer your domain to our reseller account on enom.com (well-known registrar). In this case you need to pay domain registration fee (our prices is here:
http://forum.hostony.com/viewtopic.php?t=137 )
In this case we generate domain trnasfer request to your existant registrar and domain will be transferred after receiving your confirmation. It takes from 3 days up to a week.
About the root password. We give it only if you purchase a dedicated server (http://www.hostony.com/dedicated.html).