Not much to worry about over here. You'll have to do something pretty stupid to get in trouble with the law.
I see that Bukit Chandu is on your list. Might I suggest the
Army Museum of Singapore and maybe the
Old Ford Factory where the surrender of Singapore was signed.
While you're at the Army Museum you could drop by the Discovery Centre, but I would have the say there isn't much to see at the Discovery Centre though. The Singapore Armed Forces Training Institute (SAFTI) is within walking distance of the Discovery Centre, there is a very large library regarding military subjects (
SAFTI MI Library) that you might want to check out.
I might suggest buying a bottle of water or something before heading to the Zoo or Night Safari, as the prices of food there can be quite high.
Right now is the Chinese New Year period (3 Feb >) so there should be quite a lot of things to see.
The weather over here right now is wet, it has been raining everyday for the past week or so.
When taking a cab ensure that the cab uses the meter, touting is illegal and there are plenty of signs at the airport to remind you.
Beware when buying consumer electronics (ie. digital cameras etc.), as shops here can be rather dishonest to tourists and their own countrymen alike. You'll be safer purchasing from the larger electronic superstores like Courts, Best Denki, Harvey Norman and Challenger.
Hope you enjoy your stay.