I think I saw this school when I was in SG, but it looks like one of those training schools because there doesn't seem to be any form of accreditation listed on their web site.

It might be OK then again it might also be one of those glorified baby sitting training centre for pushy SG parents.

Is the 3600SGD before tax or after tax?

If it's before tax then you might end up with about 3000SGD
Probably liveable if you share an apartment.

Cost of living in SG is here
http://www.numbeo.com/cost-of-living/country_result.jsp?country=Singapore