Advanced Permissions / Composer elements

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I like to disable certain composer / concrete edit setting for a usergroup that I created. I would like that a user in that usergroup can add a page and only add content with composer (I made certain fixed blocks they can add.. some text, attributes and a main image). So they should not have a option to add block or edit the page with the pencil icon or + icon. Also they should be forced to publish the page with a start and end date.

Do I have more options in advanced permissions or do I need to edit the core files and hide the different elements/buttons. And if so, which ones and can I make it so that certain elements are hidden from a certain (or multiple) usergroup(s).

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