Driving a Singapore car into Malaysia especially for a non local is definitely not recommended. Mainly for safety reasons cos Singapore car is always a target (supposingly rich and non locals) in Malaysia.
It is like driving a HK car into Shenzhen, can you handle it??
Driving within Singapore is ok thou, it is very small. You can be far wrong, much easier in fact cos the taxi is hard to flag.
Driving in Singapore is definitely safe! I found it very convenient. The only concern is that you have to make sure you have enough money in the NET card for toll payment.
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All things wise and wonderful. The Lord God made them all. Cecil Frances Alexander 1818-1895