The passages where the Bible and Jesus say that God answers prayers are quite numerous.
James 1:5, 1 Kings 3:5, Job 22:27, Jeremiah 29:12, Job 33:26, Psalm 91:15, Psalm 145:18, Psalm 65:2, Jeremiah 36:7, Zechariah 13:9, Matthew 7:11, John 14:13, John 14:14, John 15:16, John 16:23
And are there limits on these requests?
Matthew 17:20 And He said to them, “Because of the littleness of your faith; for truly I say to you, if you have faith as a mustard seed, you shall say to this mountain, ‘Move from here to there,’ and it shall move; and nothing shall be impossible to you.
Doesn’t sound like much restrictions on that to me.
BUT…
I don’t believe that God EVER broke or contradicted the laws of nature by which He made the world to work. That doesn’t make any sense to me. He made the laws of nature for a reason, and I don’t think He is going to break them, especially not just to impress a bunch of ignorant savages who don’t understand the laws of nature in the first place.
You believe there was magic in the past and not now, while I don’t believe there was ever any magic to begin with. I just believe there is an irreducibly subjective aspect to reality which is somewhat effected by what we want and believe, which is not the same thing at all. In other words we experience reality differently. Back then people saw supernatural events caused by God, animating spirits, disease causing demons, and works of magic everywhere. Today most of us see miracles of God and science which are somewhat confined to the context of a vast universe governed by laws of nature, and magic only in magic shows by very clever magicians for entertainment only. But the only thing which has changed is us and how we understand the world.
So can faith move mountains?
Yes, exactly the same today as ever.
By magic and supernatural powers? I don’t think so.
By unexplained events and coincidences not precluded by the laws of nature? Yep.