Because it's easier for clients to if the system is what they want from actually seeing what has been developed, or what is being developed rather than documents or models.

Because they are part of the team.

There is no need, the client will see what has been completed at the end of the project.

in case new requirements or changes in the business environment have come up and then they can be added even though the iteration isn't finished.

in case priorities have changed, since the last time you saw your client.