Congrats!! Just to add on what @carinatan has written, insurance companies only start coverage from second trimester. Can take a look here to see more!
http://molobok.blogspot.sg/2016/10/maternity-insurance-plans-in-singapore.html?m=1
Hello, yes PruFirst Gift provides coverage for your wife and child in terms of congenital defects and premature births. There are at least 4 other companies who do that. I've share some thoughts about it on my blog here...
Yes, the plans are generally the same. Since the premiums are affordable it's best to get one, especially to cover the baby from the moment he/she is born..