How to disable 'promote to front page' and 'sticky' options? Two possible methods that I have explored:

Use hook_form_alter to unset both options on node edit forms. But on the main admin content page, the options still appear under 'Update options' dropdown.

Use Override Node Options module. This provides granular control, but it means disabling the 'Administer content' permission. Users then can't see the 'Update options' at all, which they still need in order to bulk publish, delete, etc.
There are 3 places, where those options can be seen:


on admin/structure/types/manage/article, for the "Article" content type  


on node/2/edit, for the node with ID equal to 2  


on admin/content, between the "Update options"  




If you need to remove the options from those setting/administrative pages, then you need to alter the following form builders:


node_type_form()
node_form()
node_admin_nodes()


node_admin_nodes() is the form builder for the node administration overview in admin/content, which includes the "Update options" field that allows the users with the right permission to promote/demote a node from the front page, and to make a node sticky. The field lists all the node operations implemented by modules; in the list of the operations obtained with $operations = module_invoke_all('node_operations'), those operations are represented from $operations['promote'], $operations['demote'], $operations['sticky'], and $operations['unsticky'].