Grab is the equivalent. Tends to be slightly cheaper than taxi but fairly close. You can also order food from it. Useful all over South East Asia.
Go pick up a SIM(eSIM) unless you're literally there for a day. You get around 100 GB for $12 SGD, usually easily beats out roaming costs.
Keep some cash for the smaller hawkers and stalls if you plan on visiting those. Otherwise you can tap at most stores.
PT is very solid and exceptionally cheap. You can either get one of the various fun EZ Link cards or charms or just use your lowest foreign fee visa/MasterCard/Amex.
Lots of Aussie cafes (or Aussie style) so if you miss Melbourne coffee you can definitely find good ones in Singapore.
It's a melting pot of stuff globally. So you can also find US chains, Japanese chains, Chinese chains, Taiwanese etc.