A. No, typically when changing a domain name you do not need to modify any of your content. The only time you need to is if you have any URLs using the full path of the old domain, then the URL (exa: links) would need to be fixed.
A. If you transfer your domain name then you will no longer have the old domain name,
and people will login at the new domain name to access their members area.
If you do a piggyback domain then you keep the old domain,
and people would login at the old domain, not the new piggyback domain.