The only portion of the Godhead that scripture refers to as "the Word" is not the Holy Spirit but rather God the Son. Not only that but Jesus Himself repeatedly stated that He came from the Father, which is not to say that you're incorrect about it being the Spirit of God that descended upon Mary.God is Spirit.
"God is spirit, and those who worship him must worship in spirit and truth.” (John 4:24)
Gods seed is his Living word the Holy Spirit.
Gods seed/ Living word was the seed that got Mary pregnant...his seed is Alive and Active.
Now my new friend....if you don’t believe that...then there will be no discussion between the two of us.
That's all a bit of a sticky issue because there is an importance sense in which all three are the same thing and scripture is not explicit about how the Trinity works. I suspect this is because it is sufficiently outside our experience that there wouldn't be anyway for it to be explained. It could also be that we just don't need to know and God decided in His wisdom to leave the mystery intact. Regardless, in one sense or another, everything you stated here is correct. What it has to do with what we're talking about, is not clear to me but whatever.
Galatians 3:20 Now a mediator does not mediate for one only, but God is one.