Ok, crisis resolved, found the solution for the biggest new issue. 99% my own fault - incorrect setup, I was misled due to being logged in as administrator, and testing via regular user account didn't run well. Anyway, let me try adding the php code now.
So, I added the code (using Snippets plugin), but nothing's changed. (I only added a couple pages' slugs into the array, my-account being the key one.)
Is there perhaps anything I need to setup in the Post Groups settings (in Access Control)?