In a sense, this is a triune understanding because you are saying both, and the Spirit does not lead away from one or the other. "One in purpose" may seem an Arian/Unitarian statement, but it is an explanation of John 10:30. Such a statement, I don't believe, is Arian/UnitArian. It has to come from a Triune (Trinitarian) position because of the dual nature of the oneness. I realize a Unitarian/Arian tries to differentiate, but they are actually emphasizing the oneness between Father and Son here. Further, they may not recognize the Spirit as a Being, but it is yet very close to Triune (Trinitarian) expression.
"It" has an impersonal implication. Other languages can say this better but we have to adopt the masculine "Him" or feminine "Her" to differentiate. For this, most Christians will have said your sentence thus: "Of course He is. He is not visible, but Spirit-invisible." <-- Does this reflect accurately what you are saying? Thanks.
It is. You've said "One" God for instance, so math is important and part of this discussion. I also believe the nature of God, and the nature of the Lord Jesus Christ requires Algebraic expression specifically because God has not given us the values for some of our expression. Because of that, you might say a Trinitarian is trying for an Alegebraic expression of the relationship between Father/Son/Spirit. An Arian/Unitarian is rather, using a Basic (simple) Mathematics expression. The Trinitarian (Triune believer), is disagreeing that scripture presents God this simple.
Sort of, I'm being pedantic, because it shows both where we agree, as well as where we differ, and that is important. Does the difference between Algebraic vs Basic appreciations, by example, assist with your understanding why it is more complex to us?
Again, thank you for your patience. -Lon