Hello Shiv,

If you add a rule as per your 1st step then users will be able to Edit the records. So of course they can make change in deadline, description, assign to other users etc...

 If you give edit rights then & then users will able to add summery / timesheet entries into task. and If they are able able to add/modify/delete entries in summery then other fields of task must be editable. the feature you want, might be impossible to acthieve from record rules.

So you need to think from some custom way, For example,

1. You can add a group and add those fields under that group. So only some persons can edit those fields of task ( Deadlines, decription, user,name etc..) Then you can give editable rights to task. Now evenif, as per your 1st point, user is able to edit the task, those fields ( Deadlines, decription, user,name etc..) will not be editable. So user can add only task summery.
2.  You can create Custom form view, and show that form view to those users which are not supposed to edit other fields except the task summery. Hide main task FORM view from those users. Add that new menu under that group, so only some of users (high level users) can edit all the fields of task.

Let me know if you have further questions,

Regards,