Confused, sounds quite strange to me, to the degree of somebody not wanting to tell you the full story... for one thing, SIR definitely needs your signature for an EP application, plus a whole load of evidence on who you're working for, how much you'll make, yadda yadda.
Are you sure the company really is planning on transferring you? Do you have any 'independent' contacts at the SG office who could ask around for you? If you have no other options, then call HR in Singapore directly and ask them what's up. If they keep waffling, assume the worst.
It's completely unethical and unreasonable for a company to keep an employee on the edge of their seat for half a year, and also a bad sign. This happened to me once, and I went ahead with the transfer anyway, only to find myself in a job completely different from what had agreed (orally!) with half the (orally!) promised benefits gone. Fortunately, I had to get my visa renewed halfway through, and was able to counter-extort them by threatening to not renew it.

After that gig was up, I changed companies and am very happy I did so.