Faith vs God's Will

I have recently been studying the topic of faith in the scriptures and came across two passages which seem to contradict. The first passage is the Savior teaching His Apostles about the importance and power of faith.

 22 And Jesus answering saith unto them, Have faith in God.

 23 For verily I say unto you, That whosoever shall say unto this mountain, Be thou removed, and be thou cast into the sea; and shall not doubt in his heart, but shall believe that those things which he saith shall come to pass; he shall have whatsoever he saith.

 24 Therefore I say unto you, What things soever ye desire, when ye pray, believe that ye receive them, and ye shall have them.
(Mark 11:22-24)

The second is in Paul's second letter to the Corinthians.

 7 And lest I should be exalted above measure through the abundance of the revelations, there was given to me a thorn in the flesh, the messenger of Satan to buffet me, lest I should be exalted above measure.

 8 For this thing I besought the Lord thrice, that it might depart from me.
(2 Cor 12:7-8)

On the one hand we are encouraged to have faith. And if our faith is sufficient then we will have whatever things we pray for. Presumably there is a caveat in there that if our faith is so great we will not be praying for trivial things like briefcases full of money, etc.

 10 Remember that without faith you can do nothing; therefore ask in faith. Trifle not with these things; do not ask for that which you ought not.
(D&C 8:10)

But assuming we are only asking for "reasonable" things we are told quite plainly that we "shall have them."

On the other hand, we are told that the Apostle Paul had a "thorn in the flesh" that he prayed to have removed three times. I think we can safely assume that Paul had great faith. So why wasn't the thorn removed?

It is not clear what the "thorn" was. After doing a bit of searching it seems that most people believe it was either some kind of physical infirmity (sickness, poor eyesight, etc) or it referred to something like persecution or temptation. The bottom line is that we do not really know. In any case it is something that he would have liked to be spared from and he petitioned the Lord about it but his request was denied.

This is a topic that has always been of great interest to me because I was born with a physical disability and I have petitioned the Lord many times to be healed.

I think the answer to this dilemma is contained in verses 7 (above) and 9:

 9 And he said unto me, My grace is sufficient for thee: for my strength is made perfect in weakness. Most gladly therefore will I rather glory in my infirmities, that the power of Christ may rest upon me.
(2 Cor 12:9)

The Lord acknowledged that he received Paul's request but told him that the answer was "No." And the explanation reason given was that the thorn was necessary for two reasons. First, "lest [Paul] should be exalted above measure" and second, "[Christ's] strength is made perfect in weakness." Apparently Paul would have become too prideful if he did not have his thorn. And I think it serves God's purposes better to have his message delivered by imperfect and "weak" vessels.

The importance of weakness in keeping us humble reminds me of this passage in Ether:

27 And if men come unto me I will show unto them their weakness. I give unto men weakness that they may be humble; and my grace is sufficient for all men that humble themselves before me; for if they humble themselves before me, and have faith in me, then will I make weak things become strong unto them.
(Ether 12:27)

Sometimes we are given trials or weaknesses because without them we may stray from the path. So although we view them as weaknesses, God uses them to create in us great strength.

And regarding using those who are imperfect to preach God's message, Paul wrote this in his other letter to the Corinthians:

 27 But God hath chosen the foolish things of the world to confound the wise; and God hath chosen the weak things of the world to confound the things which are mighty;
(1 Cor 1:27)

If David had been a professionally trained soldier when he slew Goliath instead of a youth then it would not have seemed miraculous (1 Sam 17:33). But because David was young and inexperienced it allowed God to show forth His power when Goliath was defeated (1 Sam 17:45-50).

So when we petition the Lord for something we need to remember that we do not always get what we ask for. I think most of the time it is because we lack faith. But sometimes it is not because we lack faith, but because it is better for us in the eternal scheme of things if the request is denied.

I think there is great comfort in knowing that. In particular if we are asking for a loved one to be healed. If we have sufficient faith but the answer is still "No," we can be certain that is God's will.

 48 And again, it shall come to pass that he that hath faith in me to be healed, and is not appointed unto death, shall be healed.
(D&C 42:48)