When in Singapore you have many options for staying in touch with everyone.
Buying a SIM card can be a good idea. Many prepaid cards offer calls to Bangladesh at the same rate as calls to Singapore. The major companies are:
The SIM cards are available throughout Singapore including Changi airport and various convenience stores like 7-11 and Cheers. You will need your passport to buy a SIM card. Be sure to check for special offers. Tourist only deals are good but may not be the best fit for your needs.
The companies listed above also provide prepaid internet services with SIM cards, microSIM cards and USB dongles.