I am curious as to the "wrestling hand-to-hand with Satan" [Jude 1] - I always understood it to mean they were arguing over Moses' body, not in active combat.
Yes, they were wrestling over Moses' body; I guess I would call that hand-to-hand combat, but I suppose I should have said face-to-face.
I don't really see prayer as a way to make God do things, but more of a way of communicating to Him our deepest hurts and needs and thereby expressing our need for Him in our lives and in the lives of those we are praying for.
I don't see prayer as a way to make God do things either, but we pray for and in God's will (thy will be done). Yes, it is a way of communication; of praise and worship, but it is more than that.
I sort of bulk at the phrase "power of prayer".
Well, I don't know what to say to that. There is power in prayer, whether you want to call it that or not. Many of my prayers are nothing more than "conversation" with God; speaking to Him as I go through my day; thanking Him; praising Him; worshipping Him. Prayers of "petition" are few, except of course when I am praying for the needs of others (intercession). God meets my needs daily; all of them. What he doesn't always do, is meet my "greed". He does know the desires of our heart; sometimes, we are even blessed with those. There are many kinds of prayer and many ways to pray, but when we call upon God, there is His power.
When the disciples could not remove the demons from the child, they asked Jesus why, and he replied:
Mar 9:29 And He said to them, This kind can come out by nothing except by prayer and fasting. The bible also says we should ask in prayer:
Mat 21:21 Jesus answered and said to them, Truly I say to you, If you have faith and do not doubt, you shall not only do this miracle of the fig tree, but also;
if you shall say to this mountain, Be moved and be thrown into the sea; it shall be done.
Mat 21:22 And all things,
whatever you shall ask in prayer, believing, you shall receive.
Phi 4:6 Do not be anxious about anything,
but in everything by prayer and supplication, with thanksgiving,
let your requests be made known to God. Phi 4:7 And the peace of God which passes all understanding shall keep your hearts and minds through Christ Jesus.
Jam 5:15 And the
prayer of faith will cure the sick, and the Lord shall raise him up. And if he has committed sins, it will be forgiven him.
Jam 5:16 Confess faults to one another, and pray for one another, that you may be healed.
The effectual fervent prayer of a righteous one avails much.Elijah's prayer (what God told him to pray for) shows a certain power (no, not Elijah's power, but God's):
Jam 5:17 Elijah was a man of like passion as we are. And he prayed earnestly that it might not rain, and it did not rain on the earth for the time of three years and six months.
Jam 5:18 And he prayed again, and the heaven gave rain, and the earth caused its fruit to sprout.
This shows the power of prayer:
Mat 26:53 Do you think that I cannot now pray to My Father, and He shall presently give Me more than twelve legions of angels?
We are told to pray, to ask:
Joh 14:12 Truly, truly, I say to you, He who believes on Me, the works that I do he shall do also, and greater works than these he shall do, because I go to My Father.
Joh 14:13 And whatever you may ask in My name, that I will do, so that the Father may be glorified in the Son.
Joh 14:14 If you ask anything in My name, I will do it.
Joh 14:15 If you love Me, keep My commandments.
Joh 14:16 And I will pray the Father, and He shall give you another Comforter, so that He may be with you forever,
Joh 14:17 the Spirit of Truth, whom the world cannot receive because it does not see Him nor know Him. But you know Him, for He dwells with you and shall be in you.
And although there is much more in the bible about prayer, Jesus also taught that it is always right to pray:
Luk 18:1 And He also spoke a parable to them
to teach it is always right to pray, and not to faint,
So, maybe the problem here is the definition of "power", because for the most part I think we have similar views.
How did we get on this subject? I thought this was about ghosts?

Peace
Gracey