"I'll pray for you."

[Zarith]

Testing just proves that those things aren't supernatural. They never were. Religion teaches against such falsities. Superstition is evil. Supernatural, by definition is untestable. Think about it.

Any change to the natural world would appear to have natural causes. Without fail. Otherwise the nature of God would be false.
Likewise the likelyhood of prayer being successful. With the massive possible permutations in any given scenario, you simply cannot, as expanded upon earlier, predict anything given your complete lack of ability to do so.

Prayer for healing of the sick is answered exactly the same as any other prayer: as God wills it. God will hear your prayer. You have to accept the answer. Never ever are you given the right to change anything without Gods involvement. I find such a suggestion absurd in the extreme.

I dislike arguing from the dictionary, but you are using your own definition of the word 'supernatural', and dressing up bare assertions in appeals to "the nature of God".

Oxford

adjective
(of a manifestation or event) attributed to some force beyond scientific understanding or the laws of nature:
a supernatural being

Merriam Webster

Definition of SUPERNATURAL
1
: of or relating to an order of existence beyond the visible observable universe; especially : of or relating to God or a god, demigod, spirit, or devil
2
a : departing from what is usual or normal especially so as to appear to transcend the laws of nature
b : attributed to an invisible agent (as a ghost or spirit)

Cambridge

(of something’s cause or existence) not able to be explained by the laws of science:
From the center of the tree, a supernatural light began to glow.

None of these definitions require or imply that the event in question be untestable, unobservable, totally outside of the natural world, or anything of the sort. Rather, they say something about an event's causes.

Just as an example, by all three of these definitions, the transfiguration of Jesus would be a supernatural event, being an event that (it is claimed) took place in the natural world, but had causes existing outside of the natural world. Do you believe that this event happened? Do you have a naturalistic theory as to what happened?

You still haven't answered the important question. Do we have reason to believe that praying for a particular event in the natural world makes it more likely that this event will happen?