Conscription question

Hello guys,
A little background about myself: I have been in the states since I was 18 (2007) and naturalized as a US citizen in 2012. My ROC passport has been expired for 2+ years.
During undergrad, I have gone back to Taiwan on several occasions using my ROC passport with registration certificate, and I was able to get in/out of Taiwan with no issues.
I have graduated since and recently gained an acceptance to medical school (yay? :sunglasses: ). I am planning on going back to Taiwan before med school starts, but that means I won’t be able to get a “registration certificate,” since technically I am not a med student yet. The most I can get from the school is a letter saying that I was accepted and have paid the deposit to hold a spot in school.
My questions are:

  1. Instead of using/renewing ROC passport, can I use the US passport (for the first time) to go in/out of Taiwan for a 2 week stay without issues?
  2. What are the chances that I get caught when exiting Taiwan? (I know I might still get caught and I am willing to take the risks. I just want to know if the risk is high or low? I did not change my name and birthplace on my US passport. However, Taiwanese agencies do not know that I had green card/US passport)
  3. If I were to renew and use my ROC passport, will the acceptance letter suffice the requirements to leave Taiwan for “higher education purpose”? (like it did in undergrad with registration certificate)

Sincerely,

The man in dilemma and about to pull out all his hair