How can you schedule reports to be sent out to email addresses?

Go to Reports>Schedule. In schedule, there is an ellipsis near email address. Click that. Once there you can enter more email addresses.

Differences between timesheet approval capabilities.

If you are a Resource Manager, you can review timesheets for resources to whom you have been assigned as timesheet approval manager. If you are a Project Manager, you can review timesheets for resources who are assigned to activities within projects for which you are responsible. If you are a timesheet approval delegate for a Resource or Project Manager, you can review timesheets for resources to whom the original manager has been assigned as timesheet approval manager.

The Responsible Manager field is the Project Manager for all intensive purposes. The Responsible Manager is an OBS element where users can be assigned. Once assigned and assigned to the project, they have rights to the project as well as timesheet approval capabilities. The Responsible Manager in the OBS can be by name, by group, by anything and the respective users can be assigned.

In Team Member, I cannot see how to change expected finish date in My Tasks?

You need to add you as the activity owner in the activity and need to add in project preferences to Team Member section "allow updates to Expected Finish” Dates. Also in project preferences change to both activity owners and resources and add section or change for expected finish.

Hide when empty is not able to be checked in P6 EPPM?

The hide when empty feature in P6 EPPM is not able to be checked due to a bug in the applicaiton. There is a Knowledgebase article (Doc ID 2088764.1) which indicates that a similar issue was fixed in 15.2.4.