I Cannot Edit the Project Schedule as a Project admin?

Project Administrators should be able to edit projects at any time (including the schedule). 

If you cannot see these 'edit' buttons as an admin you will notice this little icon here:

This means that someone has checked out the schedule in MS Project and they haven’t checked it back in.

You can Discard the check out by clicking on this arrow. However if someone is working on this schedule in MS then any changes will be lost by discarding it as they will not be able to check it back in.