First of all, I'm not sure how you have staying here for 7 years unless you have been a full time student the whole time. Assuming you have been a full time student for 7 years, you have no practical experience and only theoretical academic experience. I'm not sure if you would have a chance, unless, of course, your specialization is in a niche area that the government desperately needs. But given that you are taking your courses in Singapore Uni's, I would assume that there would also be local competition, therefore putting you on equal ground with local's with the same qualifications. If that were the case, I don't see them giving you PR.
As you have not relevant experience in the field, but not here on the Family Ties scheme, you would almost have to be under the PTS scheme for PR. If that is the case, then your NS obligation would, in normal circumstances, be waived. But as you have had the benefit of 7 years of local tertiary education here, You "might" be required to do NS. But normally this would not be so.
Good question, and I cannot give you a definitive answer.