Working Together

I've been struggling with how to handle praying for things when I haven't received a promise that they'll come to pass. I can get really depressed if I'm praying for something that I know could never happen because God doesn't force people to do anything. I always say that when a situation seems impossible, God makes the impossible possible. But how can I hope in that when the impossible might remain the impossible due to the fallen nature of this world? For example, God has given me no promise that China will ever stop persecuting Christians or that its government leaders will repent and try to turn their country around. Yet I'm supposed to pray for them... right???
After thinking about things, I'm not so sure I need to be praying for Christians in China. I'm not so sure we're supposed to try to cover absolutely everything in our prayers. To the best of my knowledge, Jesus never walked into a village and asked all those who needed to be healed to come forward. Instead, He dealt with those who came to Him or were brought. In fact, perhaps when the Bible says He couldn't do many signs and wonders in Nazareth because of a lack of faith, maybe this means that people didn't bother to bring their sick to Him, not that He refused to heal the sick who came. Actually, I'm guessing those who came were demonstrating faith just by coming!
All this to say, maybe we're just supposed to pray for what God brings us. This "bringing" can be in the form of people who we come into physical contact with and God puts them on our heart, or it could be a picture in a magazine that jumps out at us, or simply a burden God gives us. However He does it, if God tells me specifically to pray for something, I can be confident that there's a reason, even if I never see it. That helps. It also helps me not feel like I have to pray for absolutely everything, and therefore feel guilty if I don't pray for any martyrs for weeks.
You know, this makes me feel more like I'm joining in Christ's work, instead of begging Him to work. Though I'm not always sure what prayer does, God and I are doing something together, and that's a fun thought.