Hi Gonzague,
When you say the User can access see the schedule on project web app, and update his tasks
does it mean the user can update the tasks inside the project plan? If so, you cannot achieve that. However, the users are able to provide updates via the MyTasks/Timesheet functionality. These updates may be automatically incorporated in the project plan,
if the project manager sets specific rules for that so the updates are automatically approved.
With regards to the second bullet point, you will need to enable ProjectServer permissions mode and then change the user permissions for the Team Members group (or create new group preferably) and enable the corresponding permissions (e.g. Open Project,
view project summary in project center) for the selected categories (e.g. MyTasks? maybe)
Hope this helps
Paul