It cannot be emphasised enough... Singapore is quite possibly the safest city on Earth. It's clean, well ordered, law and order is completely under control (See: Singapore Laws). If you get lost, just don't panic, Singapore is a multilingual society and everyone speaks English (Mandarin, Hindi, Malay and many others can also be heard).
The trade off for living in what some might consider to be a sterile society is a very high degree of personal safety. There is enhanced security at key civilian installations. Extremism is all but unheard of. Religious or racial tensions have no place in Singapore and the government takes swift, decisive and severe action against drug traffickers etc. Civil unrest might as well be nil and any public demonstration must first be authorised with a police permit.
Naturally, you should exercise the same precautions with your money and valuables as you would at home. Be smart and streetwise wherever you are in the world. Pickpocketing is not unheard of, even in super safe Singapore.
It should be noted that piracy is not unknown in the waters around Singapore.
Smoke haze can be a problem from July to October and might affect those with respiratory issues. You can keep informed about the current conditions at the National Environment Agency.
Singapore consistently tops the regional personal safety charts with studies such as the Mercer Survey... so just enjoy the city and don't worry.