Amy, you posted three different events which seem to be for different actions...
Can you list the specific process in question, along with the mapping details, and the user and role membership that is trying to create this ticket through email?
The first event looks like an error trying to start a new process while the 2 following look like UPDATE: mapping errors.
I'd like to see the specific event that occurs when you switch yourself to an Analyst and attempt to create a new instance of a specific process through email.