Please help me to respond to some of my non-trinitarian friends

I like to describe the Trinity in terms of 1 Timothy 2:5, There is one God and one mediator between God and mankind, the man Christ Jesus. IOW, Jesus is God in the human dimension. The Holy Spirit is the way God indwells believers per 1 Corinthians 12:13, We were all baptized by one Spirit into one body. We can denote the Trinity by the use of three prepositions: God the Father is over all creation (EPH 4:6), God the Son is Immanuel or with humanity (MT 1:23), and God the Holy Spirit is within all believers (EPH 1:13).

All God is saying here is that they didn't know his name- it doesn't address the erroneous logic I pointed out.

The definition of betweeness is a point on a straight line that is inside two distinct points on that same line. The two distinct points are God and mankind and Jesus Christ is in between as a mediator.

It is biblically better to describe the mediation of Jesus in terms of relationship rather than geometry, especially because Jesus is both God and man, meaning that insofar as God can be manifest (pun intended) most completely, that man is Jesus.

Three collinear distinct points are necessary for there to exist betweeness. If Jesus was the Father or God Almighty, a mediator would not be necessary. Just common sense.

He would if Jesus were also human.

If Jesus was the almighty God, the Father, and also human, then we have a single point. In that case there is no inbetweeness and a mediator would still not be necessary. Since there is a mediator, the three points are uniquely distinct.

So, your need is to explain how the uniquely distinct points are uniquely one. The best way to do that IMO is by substituting spiritual relationships for physical geometry.

I would get into a study of the Word and look for scriptures that specify the question you are asking. Look for illustrations where Jesus is being baptized and God in Heaven speaks and the Holy Spirit in the form of a dove, or even where it says, " For there are three that bear record in Heaven, the Father, the Word, and the Holy Ghost, and these three are one." - 1 John 5:7

It is difficult for us to understand "howness" very completely regarding almost anything (cf. JN 3:8), so we must be satisfied with sufficient understanding of "thatness".

In this case, we understand that the Bible teaches THAT Jesus is both God the Son and fully human (per HB 2:14-17) or Mediator (in terms of 1 Timothy 2:5).

IOW IMO, Jesus is God visible in the human dimension (the ultimate theophany), the Holy Spirit is the way God indwells believers (per 1 Corinthians 12:13, in connection with God's Word per JN 14:17 & 1JN 5:6) and we can denote the Triune relation by using three prepositions: God the Father is OVER all creation (EPH 4:6), God the Son is Immanuel or WITH humanity (MT 1:23), and God the Holy Spirit is IN all believers (EPH 1:13). Hope this Scripture-based explanation is satisfactory.

Not really. According to my friend, there are a lot of truths in your post.
IOW IMO, Jesus is God visible in the human dimension (the ultimate theophany)
According to my friend, our reality is in the mind of the Father. The Father creates many realities, and in our reality, the Father first placed His only begotten Son (the Word) in it. The Father fills His Son with His Holy Spirit. In Isaiah 63: 9-10 the Holy Spirit is described as the angel of His presence. He is described as an angel because he can be sent. Where the Holy Spirit is, the Father is. The Son recognizes that the Father is also his God. Even though the Son's will can differ from the Father, because they share a very deep love for each other, the Son obeys the Father. The Father fills His Son with His Holy Spirit so that the Son becomes the temple of the Father. That means that the Father resides in His Son's being. The Holy Spirit is portal through which the Father enters through in order to enter the being indwelled. When a being is so indwelled, the Father fills that being with knowledge of His will, the love that leads to obedience, understanding, and the power to perform His will. Through His Holy Spirit the Father speaks to and through those indwelled. In the beginning was the Word, the Word was with God, and the Word was God. The Almighty God the Father has no beginning. His existence is timeless. When a beginning came to be, the Word was there. This was before anything was created. Our reality was created by the Father through the Son He indwelled and for His Son. Together they created our reality. The Son is the visible image of the invisible God (the Father) because the Son is filled with the Father's presence and the Son obeys the Father. In Jesus' prayer to the Father before the Romans came to get him, he says not my will but yours be done. This proves that the Father and Son have different wills, and the Son acquiesces his will to that of the Father. When Jesus Christ ascended to heaven to get glorified by the Father, he was given a spiritual body made up of those souls chosen by the Father to trust in Jesus for the forgiveness of sins, and receive His Holy Spirit through which both Father and Son reside. Eph 2: 18 "For through him we both have access in one Spirit to the Father." When we get baptized in the name of the Holy Spirit by the Son, we become temples of the Son who in turn is the temple of the Father. Jesus is the mediator between God and mankind because it is through Jesus' baptizing with the Holy Spirit that we can get access to the Father. When we receive this portal called the Holy Spirit of the Father, we get connected to the Father and Son and become One with them.
Is God the Son the same being as God the Father?

The "God" part is the same being, but the Son and Father (and Holy Spirit) parts are different roles or ways of relating to humanity by the same God/Being (I Am).

Are you preaching modalism which is considered heresy by the Church before the Council of Nicea in 325 AD? Modalists believe that there is only one God with three different masks or roles (Father, Son, and Holy Spirit).

Our understanding is somewhat similar. In my understanding, the Father is the always existing Almighty God of all realities. In our reality the Father places a living, thinking, feeling being in it and calls him His Son. The Father interacts with our reality through His Holy Spirit which in Isaiah 63: 9-10 is described as the "angel of His presence'. Angel because it can be sent, and where the Holy Spirit is, the Father is. The Father's Holy Spirit is a portal through which the Father enters the being indwelled in order to communicate His will, fill the being with love, reveal truth, speak through, and empower to accomplish His will. The Father fills His Son with His Holy Spirit to such a degree that the Son, even with a different mind and will, becomes the image of the invisible God, the Father. This happens because the Son obeys the Father perfectly. Our reality was created by the Father through and for His only begotten Son. The portal that connects us to the Father and Son is the Father's Holy Spirit. The Son is the temple of the Father, and we are the temple of the Son. Thank you Father for your love and grace, and thank you Jesus for sharing your love for the Father with me.
John 5: 23 That all men should honor the Son, even ( that is ) as they honor the Father. He that honoreth not the Son honoreth not the Father, who hath sent him. The Son is our God, our Savior, and our Lord in our reality, but the Father is the One God of all realities (including ours).

My friend refers us to Gal 4: 14 where Paul refers to Christ as an angel.
Gal 4: 14 And my trial, which was in my flesh, ye despised not, nor rejected, but received me as an angel of God, even (that is) as Christ Jesus.

the word angel is contextual with the "Messenger." not an angel. But the one who is speaking from GOD receives the same as all others because it is GOD.

No, I believe the NT teaches what might be termed "relationalism" as follows:

The OT Shema (DT 6:4) teaches that God is one, and the NT also affirms that there is one God (EPH 4:6, 1TM 2:5). However, the NT teaches that God relates to believers in three ways simultaneously: as the Father, as the Son and as the Holy Spirit (1x1x1=1).

The Father/Parenthood of God is indicated in Jesus’ model prayer (MT 6:9), throughout the Gospel of John (3:35, 5:17-18, etc.), and in the epistles of Paul (RM 4:11, 8:15, PHP 2:11). God the Father and Christ’s Sonship are discussed in Hebrews 1:1-4. The Son of God also is mentioned by John (JN 1:14, 3:16, etc.) and by Paul (RM 1:4, GL 2:20, 1THS 1:10). The Holy Spirit is mentioned in three successive chapters in John (JN 14:26, 15:26, 16:13), frequently in the book of Acts (ACTS 1:5, 2:4, 9:17, 13:2, 19:2), and in many of Paul’s letters (RM 8:4-26, 1CR 6:19, EPH 4:30) as well as in some of the other epistles (2PT 1:21, JUDE 20).

Apparently, Christians failed to explain to Mohammed (c. 610) how God is able to relate to Himself and to creation as a Triunity, and so the prophet’s teaching stressed that there is one God and implied that the Christian gospel is false. It might have been helpful for him and others who stumble at NT doctrines to discern which aspect of the triune God is the subject of various biblical statements.

These divine aspects or “persons” may be distinguished by role or ways of relating to humanity: God the Father as creator or initiator (GN 1:1), God the Son as Messiah or mediator (1TM 2:5), and God the Spirit as indweller (RM 5:5). For example, 1 John 4:7 says love comes from (is initiated by) God (the Father), Galatians 5:22 says that love is a fruit of the (indwelling) Spirit, and Ephesians 3:18 speaks of the (mediating) love of Christ (RM 5:8, EPH 2:18).

We can denote these distinctions and relationships by the use of three prepositions: God the Father is over all creation (EPH 4:6), God the Son is Immanuel or with humanity (MT 1:23), and the Holy Spirit is within all believers (EPH 1:13). A single passage that comes closest to indicating this distinction is Ephesians 3:14-19, in which Paul prays to the Father that through His Spirit of love Christ would dwell in believers’ hearts (also see 1CR 8:6).

When the Bible uses masculine words for God, it should be understood that only God the Son is human and had a sexual orientation while on earth. GN 1:26-27 states that both male and female were created in God’s image, referring not to androgyny but to personality, and Jesus said (in MT 22:30 & 19:11-12) that there is no marriage and thus no need for sexuality in heaven.

Actually, since the creation also manifests God (RM 1:20, cf. JN 1:1-3 & PS 33:6), in a sense God may be viewed as a “Quadity”. As Paul told the Athenians (ACTS 17:28), “In Him we live and move and have our being.” God as Creation is throughout physical reality (called “panentheism”). However, since this mode of revelation is impersonal, it has been de-emphasized by most Christian denominations.