I've read that a person who has diplomatic immunity can be subjected to the laws in the country in which he/she is serving if his/her government agrees to it.Don't know if it's true or not but it made sense when I read it.
Irrelevant because this diplomat serves in China, not Singapore. He was on vacation. He is not accredited to the govt of Singapore, so he would not have diplomatic immunity in Singapore anyway.
Yes, that can happen. The other thing that can happen is the diplomat’s government can yank his diplomatic status without returning him home. In other words, cut him loose.
I recall about 10 years ago the son of a Saudi diplomat in Washington got charged with DUI (and I believe assault or fighting the police).
His father waived immunity immediately and let the charges/penalties stick.