Hi.
You asked: "How powerful is it really…"
I don't hear people say what I'm about to say. I believe that Scripture shows us that we are to live in the realm of ANSWERED prayer. Not merely saying prayers with no affirmative answer. I base that on the things Jesus said. Essentially, if you ask, you will receive. (See scriptures down below this post.) It's like Jesus spoke a STANDARD that we should reach for. I believe God INTENDS us to live this way.
But the reality of things is that very few people live this way. I was one of those who prayed b/c I was supposed to pray, but I did not live those scriptures shown below. Therefore, prayer was frustrating. But I confessed my frustration over such prayers and then somehow God put me toward seeking the answer and I started praying God's will--things like "God, I want no longer to be conformed to the pattern of this world. Please transform me by the renewing of my mind." Rom 12:2…Rom 8:29…and so on. Now I wasn't just mouthing these prayers, I fervently MEANT THEM. The effectual FERVENT prayer of a righteous man availeth much. Immediately God started answering that prayer. It was then that I saw the kind of prayers that God will answer.
Unfortunately, until that point, I was only following the pattern of men and not scripture. But after that point, I can say that God answers MOST of my prayers affirmatively. I seek to pray according to the Spirit's leading into all truth. I let the Spirit guide me into the word and God will show me His will and i pray it and it happens.
"… and how to we know when prayer has been answered vs. the answer being something that was going to happen anyway?"
This is a GOOD question. There've been many times when I prayed something and it appeared as if all elements had been in place already for that thing to happen anyway. (Even if I had not been aware of those elements.) To me it is like God PUSHED me into the path of His will. YES it was already going to happen, but He wanted me to partake of it, so He caused me to partake in the way of prayer. I try to remember that I serve an eternal God.
You said:
"I thought, if christians pray and know they are receiving answers to pray we wouldnt' have to argue with nontheists. The proof is there, we can simply tesity to it"
YES. Absolutely. I believe that IS THE WAY GOD WANTS US TO BE. We should be living in the realm of ANSWERED prayer. That way I KNOW God is with me. Answered prayer is POWERFUL, unanswered prayer is weak. What testimony is it that God doesn't seem to answer the prayers of His people?
Study the scriptures (this list may not be all). They speak of answered/powerful prayer. Here are some below.
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Matthew 18:18-19
18"Truly I say to you, whatever you bind on earth shall have been bound in heaven; and whatever you loose on earth shall have been loosed in heaven. 19"Again I say to you, that if two of you agree on earth about anything that they may ask, it shall be done for them by My Father who is in heaven.
Matthew 21:21-22
21And Jesus answered and said to them, "Truly I say to you, if you have faith and do not doubt, you will not only do what was done to the fig tree, but even if you say to this mountain, 'Be taken up and cast into the sea,' it will happen. 22"And all things you ask in prayer, believing, you will receive."
John 14:12-14
11"Believe Me that I am in the Father and the Father is in Me; otherwise believe because of the works themselves. 12"Truly, truly, I say to you, he who believes in Me, the works that I do, he will do also; and greater works than these he will do; because I go to the Father. 13" Whatever you ask in My name, that will I do, so that the Father may be glorified in the Son. 14"If you ask Me anything in My name, I will do it. 15" If you love Me, you will keep My commandments.
John 15:7-8
7"If you abide in Me, and My words abide in you, ask whatever you wish, and it will be done for you. 8My Father is glorified by this, that you bear much fruit, and so prove to be My disciples.”
John 15:16
"You did not choose Me but I chose you, and appointed you that you would go and bear fruit, and that your fruit would remain, so that whatever you ask of the Father in My name He may give to you.
1 John 5:14-15
14This is the confidence which we have before Him, that, if we ask anything according to His will, He hears us. 15And if we know that He hears us in whatever we ask, we know that we have the requests which we have asked from Him.
1 John 3:22
22and whatever we ask we receive from Him, because we keep His commandments and do the things that are pleasing in His sight.