How does the driver ensure that he will receive his own order? AFAIK, a driver can reject an order, but this action will badly affect his rating in Uber's system.

I think that the rating system helps at least partially to fix this exploit (if it actually is an exploit and not a fantasy).

If you don't receive your own order, have the passenger phone cancel the request and try again. I doubt the utilization is high enough that turning on the driver app immediately accepts a random request.