Welcome to MummySG.
Most malls have a parents'/baby room but it can get crowded during the holidays. But for MRT stations, I dont't recall seeing parents' rooms but some toilets (not all) comes with baby diaper changing stations.
Not all parents room are equipped with microwave but most are equipped with hot water dispensers.
Usually when I need to wheel my pram into the toilet, I would use the handicap toilet. Some normal toilets come with "baby seats" where you can park the pram outside and carry your baby in to "sit" with you.
Hope this helps.