Kevin,
ServiceDesk 7.5 has been designed to allow you to clone the permissions of the Default groups, and apply them to your own groups. To answer your three questions with my suggestions:
1. The "Support" group is the group for basic workers. In ServiceDesk 7.5 the concepts of queues and automation rules have replaced the old model with a strict Support 1 and Support 2 escalation path. I suggest you clone the permissions from the Support group onto one or more groups containing your users (potentially imported from Active Directory). Then, use the "Manage Incident Service Queues" process under Submit Request to define one of more queues for tickets to be assigned to. Finally, you can modify Process Automation Rules to assign incoming incidents to your queues as desired.
2. I recommend copying permissions from both the Problem and Change groups onto a custom group of your choice, if you plan to combine those two roles in your org. None of the groups contains all of permissions that the other groups have by default.
3. Application User is a base default group with few permissions. I recommend using the All Users group instead, which by default has the neccessary permissions for end-users to use the General Incident submission form.
I highly recommend spending a little time reading up on these topics in the ServiceDesk 7.5 User Guide:
http://www.symantec.com/docs/DOC5721
For example, the Appendix contains a section called "Default ServiceDesk user groups" which lists the groups and even contains a listing of their permissions. You can also find details on Service Queues and Automation Rules.
Good luck!