I have cousins who because their Filipino Citizen parents became Singapore Permanent Residents had to do mandatory military service, this was 12-13 years back I don't know if the law has changed now. You might have to find the right document for the SG government website to explain why your status is exempted. May be SG police do issue such letters as your VO says, you or I might not know. Try Researching in singapore forums or try contacting the police directly.
On your Indonesian PCC situation, I feel it is better to have a RCIC than ask in these forums, I had colleague who is from one of the smaller countries Africa who but lived in South Africa from his the time he was 13, IRCC demanded PCC from his home country even though the PA never set foot in his home country after he was 13., he says his consultant helped him out. he says it takes time though which can't be responded in 7 days, recommends that you ask for a realistic time from your VO.