1. SGD500 will get you either a decent room for yourself in HDB (with shared bathroom, kitchen facilities etc) at far flung areas like Jurong, Bukit Panjang with one hour plus commute to Raffles Place. Or a dingy room for yourself in HDB (with shared facilities) at closer areas like Clementi, Ghim Moh, Queenstown and even Telok Blangah, that gives you 30 minutes commute time. Check with this forum's Classifieds for ad. Do not hire an agent as a tenant, but rather answer an ad placed by an agent representing the landlord.
2. Health insurance. Some companies cover for all of their employees so check with your HR. Otherwise you can try local ones like NTUC that are cheaper. Don't talk about BUPA, you couldn't even afford Prudential or AIA in your situation.
3. There are two possible arrangement for such rental in #1. You either live with landlord and his family, or live with fellow expats, with one of them as main tenant (which makes you a sub-tenant) and the landlord does not live with you. The best case scenario is to live with fellow young working professionals because you get more freedom without having a landlord around.
4. Cooking is expensive if you're looking into Western palate. A McDonald's cheeseburger is only SGD2. A bowl of fishball noodle or chicken nice can go between SGD2.50 to SGD3.50. A cup of local coffee is only SGD1.20. Having lunch in Raffles Place can be very expensive or affordable, depending on where you eat. There are restaurants but there are also hawker centres.