So today we have these settings in place (within Objects and Rules > Tickets > Settings):

What I dislike about this, is that this same template appears to be used for both notifying CC on 1) Ticket Creation and 2) Ticket Updates. Is there a way I can ditch this template and just use normal triggers that send to Requester + CC that are more specific (1 template for ticket creation and 1 template for ticket update).
How do I do this, do I just clear out email subject/text in this area?
Also, I noticed when testing out our current setup. If I e-mail our support address from EmailA and CC EmailB, that EmailB does not get notified of the ticket creation, they only get the actual email from EmailA - why is that?


You can refer to Configuring CC and follower permissions, for the new experience for CC. I have tried it on my end and it will no longer send notifications for CC only for followers.
Regarding the CC not receiving the notification for received requests, it's possible that your trigger for such event does not include the CCs. Please check your triggers to confirm.