This should be no problem, but please remember that the address you will be given per the welcome email is only to be used temporarily. Also I believe that some scripts and services will not work without a proper domain name.
If designer-entrepreneurs.com are the domain you are moving, it should not be any problem to use it as you have until now.
Not really sure what you mean by this.
If it is a reseller account you are wanting to purchase, the techs will want to know what your main domains name is.
If a virtual account (one domain per hosting account) they will be treated separately (each domain is the main on its account).