OK I’ll give this a shot. We humans can not come to the Father due to our sins. Our sins separate us from our Creator. We are basically in a state of claiming ‘godship’ on our own, and as such would share the fate of Satan and his demonic forces, who have done likewise (and are condemned). So trying to go to the Father directly is trying to come to him as a equal but competitive ‘god’ - which is not a good place to be for a human even against the weakest demon, not to mention the Father of Creation.
Due to the Father’s sense of righteousness, He will not accept surrender to Him, you are basically a enemy of God and will be subject to His wrath.
Jesus was sent in this world to allow us the opportunity to reconcile this. Allow us to come back to God and put the situation right 'I will be their God and they will be My people". By Jesus never sinning He was wrongly put to death by the world. This violates the Father’s sense of righteousness, so to make things right Jesus was resurrected is now superior to the world (as the world has nothing to offer Jesus to make up for His wrongful death). As such He can accept anyone in the world who comes to Him and surrenders to Him.
So when we pray we do so through our King Jesus and in His name, as He is the worthy one who has overcome the world.
The gift of the Holy Spirit, or better for this discussion, the indwelling of the Holy Spirit, is God actually in us. It is many things, but for the sake of the OP it is to help us serve Jesus in this world. It allows us to know the will of God, what the Lord wants us to do to advance His kingdom on earth. Unlike Satanic forces and forces of man, ‘God is one’ and God acts as a single entity, weather that is directly from the Father, from Jesus, from a angel, or from a follower of Christ following God’s Spirit inside him, or from the Holy Spirit Himself.
Practically speaking, it seems like the more you know the more you are expected to do. If you don’t know God that well and have a really critical situation it seems like a cry to ‘God’ will usually be heard (actually God does hear everything, but I’m talking about accepting it as a prayer), with the prayers going to the correct parts. As you know more and after the indwelling of the Holy Spirit you just start doing things in the way Jesus instructed as you know it is proper.
Jesus prayed to talk to His Father. Did you ever talk to your earthly father?