Agree that for Thailand 1-2 call is quite good with country-wide coverage. Available everywhere although at some Family Marts the price will be inflated. I normally buy mine on the street or at the phone store in the Siam BTS station.
No passport required.

I use Maxi in Malaysia. If you are flying AirAsia they sometimes have a special on a buy-on-board one. Do not recall ever needing a passport to buy.

In Singapore, I would first check with the hotel. Experience says that calls from your room are often so cheap that one does not need a SIM. Also check with your Malaysian carrier and see if they roam into Singapore. Otherwise, there apparently is a Singtel deal that sells a SIM for less than the stored value of the talk time. Should be available at Changi.

Costs from memory.

Thailand: 50 baht to 300 baht depending on talk time loaded. Note 008 gives the cheapest rates to North America and Europe. Normally 6 baht per minute to U.S. or Canada. Buy top up card at any 7-11 or Family Mart. Smile and be nice and they will load it for you since you probably do not read or speak Thai.

Malaysia: 8-10 ringgit. Top up cards available all over. Be nice and the seller will load the top up for you.

Singapore: Last I heard was 8 Sing $ for 10 Sing $ talk-time including the SIM.