Lonelyguy, Sorry to hear that you are finding it difficult to find a job. That is true for a large majority including the locals and immigrants- both and I am sure you already know the rules for F1 & F2 visa holders regarding employment. If not, keep in mind that F1 & F2 visa holders by no means are eligible to work with the exception that F1 visa holders, if pusuing a full time course load can work 20 hrs. on campus/week. With regard to F2 visa holders, you are not eligible to work @ all unless F1 and F2 visa holders have received a work permit which is given under certain cases (hardships ets.) by the Homeland department. Now, to answer your queries  and from my perspective -it is entirely upto you if you are willing to venture/risk by working on a cheque or using your SSN. I have seen most F1 students work despite the risks involved. I don't think anyone will have a yes/no answer to your question. Anyway, good luck in your job hunt.