Mark 11:22 does have unusual phrasing in it. No where else in the New Testament does πίστιν Θεοῦ appear with Θεοῦ (God) as the objective genitive (Craig E. Evans Mark 8:27- 16:20, Word Biblical Commentary vol. 34b (Nashville, TN: Thomas Nelson, 2001), 186). However, though the King James Version does have a margin notes that says that this could be translated as "Have the faith of God," it is clear from the context in this passage as well as the rest of Scripture that God is the object of faith that this command has in view. A truly literal translation of this command would not be "Have the faith of God," but rather "Have faith of God," but what this really means in English is that we are to have faith in God.
Often, in the New Testament, you have what are called "Hebraisms," which are phrases that are influenced by Hebrew grammar or Hebrew idioms, and Mark 11:22 is an example. We notice that foreigners speaking English often speak in ways influenced by the grammar of their native language. For example, Russians often drop "the" from a sentence because there is no definite article in Russian. And so you might have a Russian say "Give me keys", when a native English speaker would have said "Give me the keys." There are many examples of the genitive case being used in a similar way to what we find in Mark 11:22, elsewhere in the Greek New Testament.
The other passage that "Word of Faith" preachers have used to argue that God has and exercises faith is Hebrews 11:3: "Through faith we understand that the worlds were framed by the word of God, so that things which are seen were not made of things which do appear." They twist the meaning of these words to suggest that God framed the universe "through faith", but the obvious meaning of this passage, is that it is through faith that we understand how God framed universe, and that he framed the universe by His word (ῥήματι Θεοῦ). St. Paul tells us, that "faith is the substance of things hoped for, the evidence of things not seen" (Hebrews 11:1). In other words, we believe in things that we cannot see, and hope for things based on what we have been assured of. For God there is nothing that He cannot see, and nothing for Him to hope for that he does know for fact to be a reality. And So God is the object of Faith, but He does not need Faith, because He is not trusting in the word of anyone else with regard to anything that he otherwise does not know. However, since we did not see the universe being framed, it is only by faith, that we are able to understand that God framed them by His word. And this is not just a matter of opinion, this is the understanding that the Church has had since the time of the Apostles up to the present day.
The problem with the charismatic preachers that you mention is that they are attempting to impose on Scripture the non-Christian ideas of "New Thought" philosophy, which is connected to Christian Science, and has much more in common with Buddhism than it does with Christianity.
You can learn more about the origins of the Word of Faith Movement by watching these videos:
These videos are by a Protestant, and he says many things that we would not agree with, but he lays out the errors of the Word of Faith movement, and their history, very well.
You can also read about the origins of the Word of Faith movement in the book "A Different Gospel," by D. R. McConnell.
See also: Stump the Priest: Faith that Moves Mountains?