What is the apple mobile device Support Model?
How does apple handle issues ?
Is there help desk level 1-3?
Does apple expert have any tools to view what is on users device?
What is the best process of support?
It depends on your problem. In person, the Genius Bar is great both for Macs and iDevices - but don't try without an appointment as they are very busy.
As for contacting support, start the triage process with the link in the upper right corner of this page. That will determine what course the support will take - you will be offered options depending on the problem you detailed. And yes, Apple can share your desktop with you - if you agree, they will download a small app (which you can delete after the support call).
And, there is more than one level, but you start with level 1; if that person cannot help, they will transfer you.