light cooking - boiling water for noodles. seriously.
eating out, that is, eating outside your home. it can be cheap, however, depending on your taste, you may or may not get tired of the food if you stick to the 2-3 SGD range. a little variety will cost you a bit (in the 4-5 SGD range in the hawker centres). personally, being able to cook is always a welcome option.
one-bedroom apartments are very rare, especially the HDBs (government housing projects which is the default accommodations for everyone in singapore). moreover, such units are usually reserved for the elderly. one-room
condos are also available but they can cost twice as much.
you can find good-enough units in district 2; you could also venture further into tiong bahru, bukit merah, queenstown, commonwealth, holland to the west or eunos, aljunied, kallang to the east. you can use gothere.sg or google maps to check for commuting directions if it will help you decide. street view is available on both sites so you can get a looksie.