This question has a couple of different parts to it. But see if you follow me here:
The first step is, under Settings > Activity Plans > My Task Templates > Create a New Task Template:
Then, when creating the Task Template, select the checkbox to "Automatically assign this Task to Contacts of Type" either select the contact type from the drop down list or create a custom type. Then, when that contact type is added to a Transaction File and that task template is attached to the file that task will automatically be assigned to that person.
Part 2 of this question:
FAQ: Under Task Templates there is an auto assign (is this where I can assign the task to another agent to complete?)
Answer: YES!
Part 3 of this question:
FAQ: There isn't that option when adding single tasks.
Answer: The person needs to be a Contact with participant access to the transaction. Once the person has been added to the transaction file and been given Participant access with permission to view Tasks, that contact will be added to the Assignee box . This way you can assign the single Task to a participant of the Transaction. Within the Transaction File > Tasks > Add Task, the person will be found in the Assignee box.

