In Marketo, "branding domain" and "tracking domain" mean the same thing: the click tracking domain that appears in your emails in place of the original link.
That's distinguished from "landing page domain" and "landing page domain alias" which are terms for the Marketo-hosted LP side.
To date there is no official support for multiple branding domains. The recommendation is to use the most general brand, if there is one.
Sanford is right on this.
Once you have created domain redirects, all your LP's will become immediately available to all domains.
Here is the danger with regards to GA since, your LP template has only 1 GTM code and tag... so by default, the LP will have the same GA tag in each domain instead of a different one.
2 solutions are possible:
With regards to the UTM, this should have no impact, unless I missed something. UTM are being captured from the URL parameters in form hidden fields. This will work transparently on all domains.