Using Outlook.com, it's easy to merge an old Microsoft email account with a new one. The way you do this is in the "Manage your account aliases" section. You can set your new Microsoft email account as the primary account that you use to access email from both accounts. You would be able to access your old email through your new account.
I haven't tried it with an account that had data stored in Microsoft Health and HeathVault. I'd assume because the data was in the cloud tied to the email account it would be the same. However, I think some health data is subject to stricter standards set by HIPAA so you might want to ask if Microsoft requires you to jump through more hoops to transfer this kind of health data.