Some readers wrote in to help. Islam is not a Malay religion, thus there should not be any constraints. I've read about your requests to have a smoother Ramadan in Singapore. There are many 24-hour outlets in Geylang. Many 7-Eleven outlets also sell stuff that is halal.
Some mosques hand out food after prayers.
You can also break fast in most of the mosques. Terawih, which is usually done in mosques, can be done individually. Some void decks are also used for performing terawih. The radio station, Warna 94.2 FM, broadcasts prayer times. Let me know if the information is adequate.