Q. Is it God's will for all to be healed?

A. Yes!

And Jesus looking upon them saith, With men it is impossible, but not with God: for with God all things are possible.   Mark 10:27

Q. Is sickness God's punishment?

A. No!

The thief cometh not, but for to steal, and to kill, and to destroy: I am come that they might have life, and that they might have it more abundantly.   John 10:10

Q. Did Jesus die for our healing as well as salvation of our spirit?

A. Yes! The Holy Spirit's own commnetary on Isaiah confirms He died to pay for our physical sickness as well as our sin.

When the even was come, they brought unto him many that were possessed with devils: and he cast out the spirits with his word, and healed all that were sick: That it might be fulfilled which was spoken by Esaias the prophet, saying, Himself took our infirmities, and bare our sicknesses. Matthew 8:16,17