There is no question that faith is a key element in effective prayer. On one occasion, Jesus could not do many miracles in a certain place because of the unbelief of the people there. That place was Nazareth, which happened to be His hometown. He had done miracles in other places, but not in Nazareth. And it was because of their unbelief.
Our faith does play a part in the work of God. Sadly, there has been a distortion of this truth by false teachers who say that we make things happen, that faith is a type of force we just need to use. In an effort to counter this extreme teaching, we may swing too far the other way and end up with no faith at all.
There is a place for having faith and believing the promises in God's Word. When people ask me to pray for them to be healed, I do. But I always add, "Lord, if You have another purpose that we don't know about, then not our will, but Yours, be done." I think we need as much faith as we can muster when we come before God with our requests. But I appreciate the honesty of the man who said, "Lord, I believe; help my unbelief!" (Mark 9:24). I believe God will honor that.
When you pray, "Lord, this seems to be Your will from my understanding of Scripture. . . I believe, Lord, but help my unbelief. . . and if You have another plan, then just overrule it," that is a proper way to bring something before the throne of God.