You have quite a bit going on there.
You can have the starter bench tested to see if it is good or not.
You should check all the powers and grounds.
If one burnt up, best to check them all for any damage.
Next thing would test to see if your getting power to the starter solenoid when the key is in the start position.
As to your Hypothesis.
Is this issue related to the security system possibly?
Possibly, not sure how your security system disables the vehicle.. IE. does it kill the ignition or if it disables the starter.
Does a GM dealership need to reprogram the ECM?
If there is no issue with the ECM ( according to the shop ) there should be no need to reprogram it.
Though it might be a good idea to see if there are any error codes stored.
Could my starter be shot?
How do I get this diagnosed without costing a $$$.
By researching, watching related videos and doing it yourself.
Would a shop have difficulties diagnosis electrical issues like this?
Not if there good at their jobs, but again you have to find a qualified shop and you will pay the hourly rate till the issue is isolated and repaired.