I was employed with a startup in Singapore for 15 months and vested 15K options over these months. Now the company is being acquired by a US company though the Singapore company will stay a subsidiary of the US company.
The Singapore company gave me this deal: I do an agreement with them where I consult with them (for a couple of weeks) for the code that I've written for them, and they'll give the same number of stocks of the new company.
Both the companies are young and are not public, so I can't really tell if the value of the new shares are the same as the old ones.
What are the right questions to ask here so that I understand what I am getting into?
You'll want to know the price per share of both companies, and the ownership percentage for both companies. Also, you didn't mention if you are expected to return the shares in the original company. Assume that the amount offered to you by the new company is small and perhaps risky; two weeks of work is not much at all.
If there's a large amount of money involved, you might consider getting legal representation so your best interests are protected. However, if it's a small amount of money, be sure to act quickly and decisively so the company doesn't decide to revoke the offer.