Are you paying with cash or getting a loan? If you are paying cash I don't think you need SS number. However if you are not legally a permanent resident I believe the title company will withhold 20% of the proceeds (not 20% of profit, but 20% of sales price.) when you sell. So you do need to think about exit strategy. If you plan to get a loan then you will likely need some kind of identification number either SS number or tax id number.
The Tax ID is a basic requirement. If you are utilizing a bank in your country however, it would behoove you to sync up with a bank in the state you are investing in - not to mention general counsel in the state as well.
No, just a taxpayer id number which any business can and should get as a tax shield. A foreign partner must obtain an Individual Taxpayer Identification Number from the Internal Revenue Service. This number must be used on all tax forms and will assure the correct application of withholding taxes.