welcome to the Tiki world. Yes, it is totally possible to have different home page for Anonymous and for logged in (Registered) or any other group. Just enable "Use group homepages" preference (
tiki-admin.php?lm_criteria=Use+group+homepages ) and use this feature: https://doc.tiki.org/Groups-Management?highlight=Group+Homepages#Changing_group_Settings
For the custom error messages I would actually rather use custom error pages for status 403 (see the section
# — Apache Error Handling — # in your .htaccess file) or "Redirect on error" preference:
https://doc.tiki.org/Redirect+On+Error (please improve the docs if you can)
You can also alternatively just display the login form on permission denied:
"On permission denied, display login module"
or use the field for
"The URL that the anonymous user is redirected to when a page is not found"
You can find all these settings on the General control panel below the "Redirect on error":