No. However the DNS records will need to be changed to reflect the new MX record for each domain if the domain’s DNS is handled Externally.
Yes. You will need to enter the Glue records as ns1.mail.emailsite.com rather than the current ns1.emailsite.com. (This assumes I understand what you did originally from your OP)
No.
To do this you need to set the new Glue records, the run sudo mailinabox and answer the questions using the NEW hostname for the MiaB. That should basically be it. Well, other than issuing new SSL certs.