Dear Person(s) Who Made This Website:
While this will probably not change your site or your thinking, and while I am sure I am not the first person to point this out, much of your reasoning rests on a fatal flaw in understanding.
In the Bible verse you quote, Matthew 21:21, for example, you accurately quote Jesus as saying "if you believe, you will receive whatever you ask for in prayer."
Along with other verses mentioned on your site however, you misinterpret and de-contextualize the meaning of the words.
The question in Matthew rests on what one is placing his or her belief IN. In other words, what is the object or subject of your belief? It is yourself, the prayers, the request? The text is not saying "If you fervently believe in what you are asking for, you will receive it."
Instead it is stating, "If you believe IN CHRIST, you will receive whatever you ask for in prayer." One must first believe in Christ! that He is able to do all things according to the will of God.
Secondly, Scripture, whether Old Testament or New, is written in a didactic way, where two seemingly contradictory elements are brought together; it is meant to be read, therefore, with an eye towards paradox. (Note that a paradox is not a contradiction.) So that even a verse such as Matthew 19:26 stating that in Christ all things are possible, one must still temper those with verses that insist (that) without faith it is impossible to please him: for he that cometh to God must believe that he is, and that he is a rewarder of them that diligently seek him.
That said, God's miraculous healings still happen today. There are many, many accounts of people being healed in ways science cannot account for. For reasons known only to the mind of God, most of the healings (even the ones I know of) tend to be the REMOVAL of something, not the GROWTH of something.
People have had sight restored for example; but it is through the removal of hindrances to eyesight, not the growing of new eyeballs. Why this is, I don't know. It doesn't matter.
The idea that God not re-growing amputees limbs somehow disproves His existence is wholly insufficient to "explain away" God. It simply proves that God operates in ways different from how we would expect or like (which is also found in the Bible). He wouldn't be much of a God if He did everything the way humans did.
Creation itself (with all of its fine-tuning) is a pretty big evidentiary clue that God exists; that needs to still be dealt with, as well as many other factual and logical problems that come up for those believing in a godless universe. Even science has gotten back into the game recently with the Big Bang matching Judeo-Christian accounts of the origin of the world.
This may or may not provide clarification for you. It is true whether you believe it or not.
Grace and peace to you,