Hi Tris,
For the second issue, do the two accounts XXX@HM.com and XXX@HC.com have separate mailboxes and have licenses assigned? Normally, if the user uses the email account XXX@HM.com, it requires that he has send as permission of the account XXX@HC.com. After that, the emails can appear to come from HM.com or HC.com. If I've misunderstood anything, you're welcome to let me know.
Thanks,
Aaron