Investing with foreknowledge that property values are falling seems like a timing problem or at least a situation where my offer would be reduced to reflect this coming change.As to how much to put in as a down payment that depends more on your numbers, your risk tolerance, ability to get financing, cost of financing, etc. 

I've been interested in REI for a year or so, and am only just now finding out about the BP community and all of the resources it has to offer new investors.

You said they have half the funds though so you are offering 50% leverage or are you offering 50% of the total project cost?

Lenders can have limitations on those without a US SS # but others offer specific lending to 'foreign' nationals.

@Jonathan Greene offered great suggestions on saving for your next deal and being careful about partnerships. 

Present an Offer to Lease with your terms and conditions for the applicant to become a tenant (sign lease, pay move-in monies) by a date certain prior to 8/1. 

However right now even the highest rates we can offer you for an investment are still carrying points. 

3) What if one of the applicants applied very late but offered 200 or 300 dollars more monthly for rent and requested that his application be approved?

If you can provide us with specifics, we can offer some advice.

This would be a basic package with available options offered to each participating home owner..