Is it Necessary to Redirect the Sub-domains created for Sending Email to Parent Website URL

I have an e-commerce suppose Example.com and just like any other e-commerce we send 2 types of email campaigns.

1. Transcation Emails
2. Promotional-Broadcast Emails

Now, to maintain quality score for the domain, we are sending transactional emails via.

eample.com

But, for the promotional mail, we are using Example.net

Now, after reading a lot about email marketing, I found that you have to:

1. Redirect the second domain to the first 1 To optimize the domain authorities in Gmail's Eyes for good domain value.
2. You have to create an envelope domain so, that you can collect your bounce, spam and another kind of emails into it. Now, Again If we create a sub domain do we have to redirect that subdomain to the parent domain as well.
3. Create a Live Mailbox.

Now, the question is do I've to redirect.

Eample.net &
envelope.example.net to
Example.com

And What if the Example.com is on https do I've to buy the https certificate for the .net version as well.