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As an administrator you have full control over the roles and their permissions. You can change them in the backend of Sitefinity under Administration -> Roles. For more information you may want to refer to this article and its subsections from our documentation. For your convenience I have also recorded a short video illustrating the setting of permissions for a newly created role.
I hope you find this reply helpful. Please don't hesitate to contact us for any further questions you may have.
On your first question - after a thurough investigation we found out that this is a bug, so I have logged it in our system for fixing. You can follow the progress in our PITS.
Thank you for bringing this to our attention, your Telerik points have been updated.
On your second question - To set permissions for a custom module you need to go to Administration->Permissions->Your Custom Module. Set the desired functionalities by clicking on Change, from the menu choose Selected roles or users -> Add roles and users.
To answer your third question you need to go to Administration -> Backend Pages click "OK, Continue" . Navigate to Sitefinity->Design->Templates where you will see the Page Templates page. From the Actions menu choose Permissions and set the required permissions to your custom role. This time you should be able to see the Page Templates in the Design menu. If you want to edit the page templates with your custom role however, you will need to give permissions to each individual template by going to Design->Page Templates and from the Actions menu for each page template choose Permissions. Instead of doing this manualy for each template you can use this code: