A response to the "small group questions" for the 20 October 2019 message at First Pres, Boulder. 
Nevertheless, I tell you the truth: it is to your advantage that I go away, for if I do not go away, the Helper will not come to you. But if I go, I will send him to you. And when he comes, he will convict the world concerning sin and righteousness and judgment: concerning sin, because they do not believe in me; concerning righteousness, because I go to the Father, and you will see me no longer; concerning judgment, because the ruler of this world is judged.
excerpt from the English Standard Version of the Gospel according to John 
How would you describe the indwelling of the Holy Spirit to someone who is not familiar with this teaching of the Bible?
If anyone is in Christ, he is a new creation. The old has passed away; behold, the new has come. 
We as humans are broken relative to our purpose, and our spirit misunderstands the difference between good and evil. Through Christ we are able to return to the created purpose, and our spirit is superseded by God's, which leads us toward Good.
What role(s) does the Holy Spirit play in our lives?
The Spirit is the life God breathed into creation. Our life died when man chose to follow his will over God's; but through Christ we are able to live again, and the Spirit leads us in the will of God.
What are the different names/descriptions for the Holy Spirit throughout the pages of scripture?
I've got to be frank: I'm going to Wikipedia for this one. 
- Spirit of God
- Spirit of "Yahweh"
- Spirit of Wisdom
- Spirit of Christ
- Spirit of Truth
- Paraclete (advocate; helper)
I don't know why I haven't noticed this before; but the Holy Spirit (such as is described in the Gospel of John) is the literal opposite of the Satan in creation. The Satan is the accuser or the adversary. The Holy Spirit promised by Christ is the advocate or the helper. Both refer to a legal context, as in a trial, with הַשָּׂטָ֖ן ("the satan") being not unlike a prosecuting attorney, and ὁ Παράκλητος ("the paraclete") being not unlike a defense attorney.
One of the roles of the Holy Spirit is to convict us regarding sin. How would you define sin? How has the Holy Spirit recently convicted you regarding your own personal sin?
My understanding of the work of the Holy Spirit is that he is the replacement of our wills with that of the Father's. By giving us a spirit of Truth, a spirit from God, we know what is truly good for us, whereas before our will was broken and choses what is not part of God's creation. Part of this is a conviction of sin, where we are pointed away from the good that God has for us, so that we can recognize it and replace it with a desire for what is good.
The Holy Spirit is working in my life most recently (and, in reflection, throughout most of my life) toward having a right heart that is pointed at God and not as an accuser myself, even tangentially. I am habitually a creature of justice, and my desire is to bring the world around me into better alignment with "the good"; but when I am unable to do so (either by my own ignorance or by the fact that it is outside of the sphere of my control) I too easily allow myself to behave incorrectly out of frustration. It is a kind of worry, I think: that if I cannot bring about good outside of me, it somehow indicates a deficienty in myself. But it is precisely the worry that is the deficienty, and I must focus on having a heart after God without external dependency.
Why is it important for the Holy Spirit to convince us of righteousness?
The scripture says that the Spirit ἐλέγξει ("will convict" in the ESV; but potentially significantly more ambiguous ) of righteousness because "I [Christ] go to the Father, and you will see me no longer." Because we will not have Christ incarnate in the world to serve as an example for righteousness, the Spirit will show us what is good. He will question, check, and test our understanding of good; control, check, and monitor our pursuit of it; and audit our behavior to help us better understand the good into the future.
How should an awareness of the indwelling of the Holy Spirit affect our daily lives? In what ways has it affected your life personally? How do you hope it affects your life in the future?
My mind keeps bouncing around in scripture; but I settle most on Romans. 
I know that nothing good dwells in me, that is, in my flesh. For I have the desire to do what is right, but not the ability to carry it out. For I do not do the good I want, but the evil I do not want is what I keep on doing. Now if I do what I do not want, it is no longer I who do it, but sin that dwells within me.
So I find it to be a law that when I want to do right, evil lies close at hand. For I delight in the law of God, in my inner being, but I see in my members another law waging war against the law of my mind and making me captive to the law of sin that dwells in my members. Wretched man that I am! Who will deliver me from this body of death? Thanks be to God through Jesus Christ our Lord! So then, I myself serve the law of God with my mind, but with my flesh I serve the law of sin.
There is therefore now no condemnation for those who are in Christ Jesus. For the law of the Spirit of life has set you free in Christ Jesus from the law of sin and death.
The Spirit, sent by the Father and come in the name of the Christ, fills us with the Word and frees us from our bondage to sin. To set the mind on the Spirit is life and peace. I pray that this peace will continue and expand, that I will live more tomorrow than I do today.
|||IN the Holy Spirit: convINced|
|||2 Corinthians 5:17|
|||Holy Spirit in Christianity: Names|