Bank: You will need a DBS Bank account. Otherwise you will spend 1/2 the time searching for ATMs. Additional bank - See Standard Chartered/Citi/HSBC
Credit Card: No card gives you status miles. In fact even in the US, except AA, I believe no airline does it
Recommended cards:
Maybank horizon platinum for overseas spending
Citibank premier miles for regular spending
AMEX Rewards card for initial 16000 points for 50 dollars annual fee. Then throw away the card
FFP: Depends on your usage patterns. If you fly a lot of silkair, Krisflyer is only option. Else I recommend crediting your miles to BMI or a US-based airline.