I think your questions are very deep in the things of God. Some of God's plans are unchangeable. He is sovereign and will do certain things no matter what. These things are not dependent on man's faith.
Other times, God's will is known and He will put people in places to carry out this will. For instance, suppose a sinner, with no access to a bible asks God to bring someone to them to teach about Jesus. God's will would be to bring someone there. It may not even be the first person He asks but He will in some way get that person taught, even if God had to use angels or creation itself. This is just one example how God directs the members of the body of Christ, into positions that help fulfill the will of God. Consider another example, where I pray for a new church to emerge. Soon afterward, this happens. Now I could mistakenly think, my prayer caused this. No, it was God that ordered the prayer to begin with, and if one person did not prayer or respond, then he would likely find others. The prayer shows the person is in agreement with God's will. In your question I think this is part of how you state: "know God's plan and express it before God and humans?"
Lastly, I think there are man's plans. If they are of the flesh, or not part of God's will they most likely will go unanswered. If they are within the will of God, then certainly one should ask in faith.
James 4:2-3 2 Ye lust, and have not: ye kill, and desire to have, and cannot obtain: ye fight and war, yet ye have not, because ye ask not. 3 Ye ask, and receive not, because ye ask amiss, that ye may consume it upon your lusts.
For instance, if the Centurion never traveled to ask Jesus about getting his servant healed, then the servant would never have been healed. It would have been "ye have not because you do not ask.
Now we know that some hear the word and produce 30, 60 or 100 fold fruit. To me this corresponds with: Rom 12:2, Do not be conformed to this age, but be transformed by the renewing of your mind, so that you may discern what is the good, (30) pleasing, (60) and perfect (100) will of God. I think our prayers too, can have differing levels of faith. This may range from faith to barely get by, to praying the perfect will of God. Complicating things is that we have to have faith to actually receive the level we are praying for. When we pray beyond our faith level, the devil does not leave, or the storm does not cease. We are in presumption, not real faith.
I don't think any of our prayers really change the plan of God, His plan is already known. It is more like, what level of faith do we have to help bring about the will of God? With low faith, we barely get by, with great faith, we can move the mountains that God is seeking to be moved. This is multiplied too at the corporate level. If a church is fully believing, in strong faith, then they surely will have the fruit. The same could be said for a nation of believers. Regardless of the individual, church or national levels, faith must be based on a knowledge of God' will, and by people putting the faith into action.
It has been said (my paraphrase) that it is better to walk in God's will, than ask God to bless your will. Prayers creating human plans seems fleshly and likely will not be answered of God. Suppose too that someone prays and fasts for days for God to set them apart as a prophet. God meanwhile, has called them to teach. I suppose they might prophesy apart from the office, but without the call and full giftings of a prophet, the prayers will come up short. We are the clay and He is the potter.
In the instances where prayers or actions changed the mind of God, Isaiah 38:5 is a good example. Had Hezekiah done nothing, then he would have died. However, as he had tears, (and likely repented) God was moved and added 15 years to his life.
Lastly, I think the favor of God is slightly different from the prayer of faith. This is an entirely different question though but certainly something to thing about like how do these two interact, and how far will the favor of God bring you, versus the prayer of faith.
