Like you, I am not a Greek scholar, and so I cannot offer a linguistic assessment of your question. I accept that careful examination of the writings is necessary to ensure we understand what they are trying to convey to us. But I can't help feeling that getting technical about the Greek is missing the point. Vast numbers of believers have lived over the past two millennia without benefit of semantics, yet we can be sure they are with God as a result of simple uncomplicated belief. Maybe your JW friend is trying to catch you out by making it complex!
Trying to view this with simplicity (and hopefully not ingenuously) I can't help feeling that this issue demonstrates the poverty of human language. As Father Simon says, the Holy Spirit is referred to as masculine, as is also the Father. Yet they are spirits, and incorporeal, and hence are without gender which is only pertinent to physical beings that can reproduce.
As humans we can only understand things in our own terms. To us a person is either male or female. Neuter is indicative of something not alive. However, spirits do not conform to this pattern. Because they have no gender we cannot regard them as either male or female, yet because they are alive we find it hard to think of them as neuter. Perhaps we simply should not do so. Maybe (from this point of view at least) we could do with a different term for the Father and the Holy Ghost instead of 'He', since technically neither of them are masculine.
I fancy this dilemma was well known to the early Christians, who had to come to terms with the human maleness of Jesus (the Son of) God which was in stark contrast to the hidden spirit nature of the Jahweh of the Jews. Yet, as Father Simon also points out, Jesus referred to the Spirit as 'He' and also to 'Father/My Father/Your Father' - in His wisdom using terms that were as close as humans could cope with.
This aspect of the nature of God is yet another deep mystery that we shall probably never understand properly, even when we are in His presence for eternity. A parallel mystery is time. We exist in time, and our entire life is regulated by it and we relate every action to it. Consequently we cannot grasp the concept of eternity, which implies time without end, either past or future. It actually makes sense to think of God as existing outside of time - pure constant existence. Once we are with God, we are also stripped of our slavery to time, and live with Him constantly.
Gender and time are concepts of creation established by God to allow us to understand the world in which we live, and how we live our lives. Trying to understand the Kingdom of God and His nature in our terms is just asking for a hiding to nothing. This is a classic problem for Biblical fundamentalists, the Bible having been compiled by men who had a different view from ours, and a different perspective about the purpose of their writings.
With love and prayers,