Re: "I can do all things through him who strengthens me."

Yes, I can do all things, through Christ who strengthens me, if it's his will.

Lazarus walked out of his grave. But I guarantee it wasn't Lazarus's will that made that happen, but that happened by the will of God.

So if God wants me to move a mountain tomorrow, I can do that, by His strength. But it's not going to happen if it's not his will. He's not going to just let me decide on my own will to do it. He may not want that mountain moved. He may have a great purpose for it staying just where it is.
The bible is filled with people doing amazing things by the strength and power of God. Let's look at the story of Sara and Abraham. God promised them they would have a son, even though both Sara and Abraham were in old age, and Sara's womb was dead. God didn't tell them when though. And so they started getting anxious when it wasn't happening and started thinking that maybe God expected them to figure out how to make it happen somehow. Sara's womb was dead, so they had to figure out another way to have this son that God said they would have. So Abraham goes and sleeps with the handmade. And Ishmael was born. But Ishmael was not the son God promised them. It was not by "their efforts by natural means" that God was going to bring his promise, but by "His strength" doing the supernatural, the miracle of him making Sara's dead womb alive, that the promise was going to come. And So Isaac was born, ten years after Ishmael was born, and he was born at the time God planned for him to be born. So I'm sure Sara was saying, "by his strength, I can do all things, I can have a child in my old age!", but she learned it must be by God's will and timing.

God is going to do what he wants to do. And if he wants to do something through someone, that person can do whatever God strengthens that person to do.

Isaiah 46:10
Declaring the end from the beginning, and from ancient times the things that are not yet done, saying, My counsel shall stand, and I will do all my pleasure.

That scripture that says God has prepared in advance good works for believers to do, means God is going to give us the strength and whatever else it takes to make it possible for us to do those good works, and it will all be according to his will.
I believe that God heals people. I believe he does it in his timing by whatever means he chooses, whether it's by a miracle or by giving someone the patience and strength and guidance to stick to some rigorous natural healing protocol, or whatever other way he chooses. I also believe God sometimes says no to healing, like he said no to Paul about his affliction which Paul begged for God to take away. But I believe when God says no to his child's request for healing, he will provide strength in the weakness, and also comfort through it. I've seen God do great amazing things through illness in people. I've seen what Paul talks about here:

Not only so, but we also rejoice in our sufferings, because we know that suffering produces perseverance; perseverance, character; and character, hope. And hope does not disappoint us, because God has poured out his love into our hearts by the Holy Spirit, whom he has given us. {Rom 5:3-5)

We are not promised a perfect life in this world, but we are promised trouble and suffering.
John 16:33
In this world you will have trouble. But take heart! I have overcome the world."
Romans 8:18
For I consider that the sufferings of this present time are not worthy to be compared with the glory that is to be revealed to us.
—2 Corinthians 4:8-11
We are afflicted in every way, but not crushed; perplexed, but not driven to despair; persecuted, but not forsaken; struck down, but not destroyed; always carrying in the body the death of Jesus, so that the life of Jesus may also be manifested in our bodies. For we who live are always being given over to death for Jesus' sake, so that the life of Jesus also may be manifested in our mortal flesh.