> How safe is Singapore public transportation and walking?
Extremely safe. Even the whiniest people in Singapore (and that's a high bar to clear) will never say that Singapore is unsafe.
Once in a while I see videos of cars not stopping in front of a pedestrian crossing. These posts result in a universal condemnation.
Also note that the UK-style pedestrian crossings include a buffer space next to the actual crossing.
In terms of public transportation, you have the subway (MRT), the light rail (LRT), and the buses. All new, and most of the MRT plus LRT are automated.
Additional aspect is drink-driving. The alcohol is also heavily taxed (almost Demolition Man style: "x is not good for you. What's not good for you is illegal") and the way the government views drugs is clarified in the disembarkation cards saying "Death to drug traffickers" (and they actually mean it), and with the combination of high availability of public transport complemented with cheap taxis / ride-sharing and low availability of intoxicating the DUI is pretty much non-existent.
In the US, the sidewalks are scarce in many places. But that's pretty unique, you don't need to go to Singapore to see streets with normal sidewalks.