Hi Tim,
1. Landing pages on custom domain is available in D365 Marketing, D365 Marketing will also generate track script and you could just embed the form to landing page by pasting the script on your own domain web site as what you did in ClickDimensions.(As many people integrated it with their Wordpress)
To enable the feature:
In marketing form entity's form page, open Form hosting tab,
create track script automatically in left side "Related marketing form pages" section, add your own domain right side "Whitelist rules" section:

Open marketing form page record and copy code, simply paste it on custom domain web page:

then view submission records with domain URL in Insights tab:

2. If you choose to use portal to host marketing page, you might could only track portal host name likes: xxx.powerappsportal.com, so it wouldn't be your authenticated domain.
3. As you found, by configuring DKIM, you could send marketing emails with own domain and have pre-filling form feature.
But it's not necessary for just landing page because adding domain to whitelist is enought for this type of marketing page,
it's only required if you would like to make your own domain to host subscription center type marketing page at same time,
and if you have configured DKIM for a domain, you can use it for both landing page/subscription center without whitelist for landing page;
just as first submission record in my screenshot.(record 1 is from my own domain with configured DKIM, record 2 is a free domain by 000webhost)
(marketing form is embedded on marketing page and its the core function on page, so it could be regarded as equivalent to marketing page in some situations)
Regards,
Clofly