Singapore events and attractions open at Chinese New Year

This is "opinion only" - I cannot speak with authority on specifics but, I have visited Singapore a number of times (4 or 5?)and the following would be what I would expect based on what I have seen there and elsewhere in Asia:.

While I have seen the downturn in Asian public activity immediately after Chinese New Year (even Hong Kong gets very quiet) I'd expect this to be more related to the number of people seen in public than in major attractions open.

You can almost certainly check on a website by website basis but in Singapore I'd expect you could see "Chinese Garden" (very good gardens)(get off train at 'Chinese Garden' :-) - walk directly into gardens ),
the impressive new high tech gardens in town (I've not seen them yet),
Changi,
Zoo,
Bird Park. ... similar.
Sentosa Island is ALWAYS willing to take your $ (horrible place :-) ).

I'd expect areas like Little India, Arab Street,...to be lower populated but odds are that shops would be open and selling food.

Some temples may be less populated but probably still able to be accessed as much or as little as ever.
Mosque in little India is the most 'tourist friendly' & "laid back" I've seen anywhere (I'm Christian but I (very politely) 'evicted' rowdy tourists from the Mosque on one occasion when the locals just ignored their rudeness).

Marina Bay will still probably take your $ so you can go up and see their infinity pool and view.

Overall I'd expect that the island would be "slow" but that there would still be lots to see and do if you are only there for a few days. –

The island does indeed slow to a crawl, however, Arab Street & Little India as indicated above are both open for business. My wife's family (about 2/3 of which live in SG including her mom) have made a point of taking me (the only Gwai-lo in the family) out to see the city when it's at it's ebb during CNY, including lunch on Arab street, buying durians from roadside stands (that's a whole 'nother story), etc. Even the MRT (excellent local transit) is uncrowded. If I remember correctly the casino is open (haven't been back for a few years now).

Now compare that to the city center on CNY eve, holy cow, if you're a westerner, be prepared to have your personal space invaded! It is packed solid with people, you can't move freely, and it's a sea of black hair making it nearly impossible to locate people if they're Asian (or simply dark haired). I'm 6'-2" and can see over the majority of the crowd, but my wife is 5'-0" and can't, so she will simply wrap her hand around my belt and follow me through the crowds. If we got separated it would be nigh on impossible to find each other again, but we planned for that & set up a rendezvous place beforehand so we could meet up if it became necessary (it never has, yet). Even with mobile phones you can't find someone, even if they're within feet of you, it's simply stunning how crowded it is. Fortunately the people are all very jovial, and unless you suffer from agoraphobia, you'll have a pretty good time.