Lot of Dreams with Loads of Confusion--- Getting Job in Singapore

a. + b. Extension of an SVP (=tourist visa) is at the discretion of ICA. They will ask you for the reason you want to stay, and what you answer must be convincing (e.g. visiting relatives is good, sightseeing not - given that the average visitor is done with it in three days). While job search is allowed on SVP, the political climate is not currently favourable for it, so I'm not sure if I'd mention it. You also need to be able to show sufficient financial reserves for the sat (and a return ticket) - since (if you don't have relatives to stay with) SVP holders are limited to hotels and services apartments, this means at least S$100-150/day. You might also want to show them your accommodation booking.

c. The Singapore government does not want foreigners to come in "below their worth" and distorting the market (salary levels) for locals. Thus if they find out you under-declared your value, you will get into trouble - this can mean deportation and blacklisting from ever working in or even visiting Singapore again.
Singapore is NOT a place to beak any rules!
(And besides, even with only a B.Sc. and 3 years experience, you'd need an EP not S-Pass.)

d. Looking for a job from abroad and without personal connections is very hard. If you don't have e.g. a friend of a friend who works in your industry in Singapore and could recommend you, you might want to wait until after Chinese New Year (when the year end bonuses are paid and many people resign afterwards).