Why are so many sick?

Whe God made man, He gave man free will to either follow Him or turn away. He gave us free will, because He didn't want robots that had no choice, God is love, and He wants us to love him; you cant make someone truly love you, it must be their choice.
So man turned away, and left the protection of God, just like someone's daughter or son, if they leave home and reject their parents, you cant make them stay, and when they are gone they leave your protection and care.
So it is because we have turned away from our Heavenly Father - God, that sickness has come to this world, God did not give us sickness, and He wants us to come to Him to have it removed by His healing.

How does God heal?

When God made the world, He gave all authority on earth to mankind Genesis 1:26. We then gave the authority away to the devil by turning away from God. This brought sin and sickness and death into the world.
God then sent His only Son Jesus Christ to pay the perfect price for that sin, which has been paid on the cross for everyone who will receive it freely.
In paying for our sin, Jesus also paid for our healing, and ultimatly our lives. if we receive healing by trusting that God will heal us, we can be healed.
If we accept Jesus by receiving Him into our lives, and allowing Him to guide us, eternal life with Him is guaranteed.

Can God heal through anyone?

When someone comes to Jesus and asks to receive Him, and when that person totally means that, and continues by allowing God to fill and guide their lives, they become born-again in the spirit, and the Holy Spirit then resides in them permanently.
It is the power of the Holy Spirit that heals through Christians, but in adition to becoming a Christian, that person must also totally believe that it is always God's will to heal, and that He carries out that healing through our prayer and also with the authority and power He has given those that genuinely follow Him by the Holy Spirit.
If you are born again and believe that Jesus has already provided that healing, you too can heal.