OK, there are 2 problems here.
#1 - there is a failure to create a site using the "Program Registration" template. I just tried on my end and it works. So, questions:
1/ Make sure you are NOT creating a site on the "default" environment
2/ Can you create sites with a different template?
3/ Have you tried a different Dataverse instance ( you can now create up to 3 dev Dataverse instances)
4/ Do you have permissions to create sites, is it possible an admin has blocked this? https://learn.microsoft.com/power-pages/admin/admin-roles
If you have checked all of these and still having an issue, open a support ticket as there is something funky with the backend, and the support team should be able to see what is going on.
#2 - The Customer Self-Service portal requires Dynamics 365 Customer Service. It is an older template that requires pro-dev help to customize.
Yes, you could start from the blank template and create a site with comparable features (add a ticket, edit a ticket, view only my tickets, etc) as this would use regular Power Pages configuration. This tutorial uses a 'scholarship' example but that could easily be replaced with a 'case/ticket' type table instead. https://learn.microsoft.com/power-pages/getting-started/tutorial-dataverse-website
Hope that helps.
Cheers
Nick