These are good questions and there are some (partial) answers to them.
Remember that "metaphysics" means "after physics" or you can think of it as "beyond physics". It deals with things that do not have shape, so in that sense your question is answered by saying God does not have a definite shape that you can visualize or comprehend. This is what the Fathers mean when they say we can't know Him in His Essence.
But you rightly noted that we can visualize Jesus Christ, Who is God Himself! Of course, we can only visualize Him in His human nature, but since He is God at the same time as Man, in a sense we can say that it is possible to visualize God as Jesus Christ.
God the Father cannot be visualized in Himself, although He can be represented symbolically, and is on certain icons, as you point out, e.g. by a hand, or by the image of an old man (yes, some will dispute that those icons are genuinely Orthodox, but they are meant to be symbolic of the Father, not true depictions). This is what Christ means when He says "no one knows the Father but through the Son". I.e. we cannot "know" (visualize) God except in His Incarnation as Jesus Christ.
When it is said that "God is Spirit", that means that God is immaterial, i.e. not made of substance that can be studied or comprehended by human reason. But He does have "substance", if by substance we mean "nature". God really exists and has a nature and substance, which is Uncreated and eternal. This is what we call the Divine Nature, the nature of being Uncreated.
I wouldn't say God has a soul but that He IS soul, or rather three souls: Father, Son and Holy Spirit. In the same way He IS three minds. What is distinct about God, though, is that the three minds work in concert and never against each other, so really there is only one mind of God. By analogy, when we Orthodox pray together, we ask God that we become of "one mind". What God has by nature we pray that we can possess by grace.
The distinction between spirit, soul and body is complicated. With respect to humans such as ourselves, we have two parts, a body and a soul, i.e. a material part and an immaterial part. The "spirit" is not a second immaterial part of us, but rather a part of the soul itself, i.e. the part that possesses a rational will that is capable of voluntarily submitting to God. "Spirit" and "mind", in the Orthodox sense of "nous", are interchangeable. Other animals have souls, i.e. immaterial animating principles, but they don't have spirit, i.e. they have no rational will. They don't really have personality either, since persons are essentially free agents, and animals, though alive, are not free agents.