You need to set the Staging module permissions for given user role (here are also some details on staging security setuo). Then, to change only own tasks - there is no such a restriction to be set but you can tell the editors to use Staging task groups and stage their tasks only. But, if you want to enforce this, you will need to customize the UniGrid (similar idea described here) and add desired logic to the code or, create a custom module with custom interface. In the code behind files you will use Kentico API to list and manage the staging tasks and at the same time add your desired logic to meet your need.