INR or SGD

1) Check with your bank what would be the likely charges if you just used your credit/debit card to withdrawn SGD when you are in Singapore.

2) only if they offer currency exchange as part of their services i.e. they have a float of SGD - ASK THEM.

Thanks Gravitas. Will check with them. Is there any rule if I convert and bring sgd in cash with me?

It looks like you have to declare any amounts of hand carried cash above. S$30,000

Another question is whether the exchange rates in India for INR to SGD are better (bank or money changer) than those offered by Singapore money changers.

As a general rule, you should change your money into a foreign country's currency IN THAT COUNTRY.
Singapore money changers have excellent rates - compare a few in the upper floors of malls around Raffles Place to get the best value!