Q1) Is the holy Spirit another part of the trinity or is it the power and essence of God?
There are a few different types of Christian theology about this, and basically when you break them all down, we find Christians who believe one or the other of your statements about the Holy Spirit. Though I pitch my tent in the camp with the Christians that believe the Holy Spirit is a personal being who is God, a part of the God head, and not just an impersonal force that emanates from God, like electricity of something.
Here is why.
Jesus Himself said in Matthew 12:31, “Therefore I say to you, every sin and blasphemy will be forgiven men, but the blasphemy against the Spirit will not be forgiven men”
And a big statement is in Luke 12:10 “And everyone who speaks a word against the Son of Man will be forgiven, but anyone who blasphemes against the Holy Spirit will not be forgiven”.
The second one basically says we can get it wrong about Jesus, but we can not get it wrong about The Holy Spirit, because this is unforgivable.
So if somebody tells me that the Holy Spirit is just an energy or force, I would ask, why is it so important to Jesus that we revere and respect the Holy Spirit so much that if we do not, it is the one and only unforgivable sin? Would Jesus be so passionate about a force of energy? Not likely.
Furthermore, to me the Holy Spirit FEELS personal. The Holy Spirit talks to us personally, knows us intimately, convicts us specifically, and lives in us individually. Our relationship with the Holy Spirit is a very personal one, which we can often feel clearly, and implies that the Holy Spirit is more then just a force of nature coming off of God.
So all of this is to say that I believe the Holy Spirit to be a part of God, and is God, and was there during the creation event (Genesis 1:2) just the same as Jesus (John 1: 1-4) and the Heavenly Father (Ephesians 4:6)