1. You have a choice to send FX from the US in USD. That way you get charged the rates at the recipient account ( i.e. if your account is with HSBC you get rates used by HSBC in SIN). My experience is that this gives better x-rates than translating into SGD in the US itself. (During wire transfer you can specify if the recipient account is USD). Unfortunately in addition to ccy conversion charges ( often 1-3%), you also pay a fixed charge for every single overseas credit to your account. So my suggestion, if you can afford it, is to transfer once, together.
2. USD denominated account - yes you are liable for x-rate fluctuations each time. Probably not the right approach if you ask me. I see no benefit from this.
3. Foreign wire - the best way I've found is DBS bank. They give you the option to transfer to BoNY in NYC thereby costing you only $10 as opposed to the usual $30-40. I've personally found this most reliable.
Details here
[URL="http://www.dbs.com.sg/sg/personal/payment/additionalinfo/faq/inward/answers/#7"]
4.Credit Card in SIN - typically with a job you could get a cc with 2X your monthly pay with no credit history. Banks are typically not as rule bound as in the US and will consider your situation on a case by case basis.