This has always been a fascinating question and I find myself thinking about it probably more than I should. But who cannot get excited when contemplating Isaiah 6, Revelation 5, and other like passages?
God the Father is a Spirit as Jesus said and therefore invisible to fallen man as is the rest of the spirit world unless God Himself opens our spiritual eyes as He did for John and Isaiah, and other lesser examples in scripture such as the young servant of Elisha. He is not physical in any way and is not bound by a body of any kind and is non-corporeal. I think this is clear from scripture.
At the same time, I cannot buy into the idea that God the Father is limited to invisibility or formlessness (even in spiritual realms where we have never been and cannot comprehend) as do Hank Hanegraaf and others who tend to lean toward allegory when confronted by such passages. I am far from a wooden literalist and allegory is often the right way to go but to me that view is a forced one that conveniently allows for human logic and permits an explanation that is comprehendable to humans. I don't know how anyone could take such a view and claim authority, given the limited attention of scripture, the obvious limitations of our fallen nature, the time-space continuum, and other factors.
I certainly don't know but I suspect that God the Father has the ability to appear in a spiritual 'form' just as reported by Isaiah and John and others and that He may do so 'again' (a time-space term) with His church gathered before Him as indicated in the scripture. Maybe not, but I wouldn't be at all surprised if the scene is precisely as revealed to John and Isaiah, just as I wouldn't put it past God to have real, physical streets made of pure gold in The Holy City. 'Form' is not a perfect term but the word I might prefer doesn't exist in the English language as far as I know. I think 'body', even 'spiritual body', definitely portrays the wrong idea and would agree with Hanegraaf and others on that point. When, how, how often, or why God the Father may manifest Himself in a spiritual 'form' that could be distinguished by creatures He chooses, I have no earthly or heavenly idea.
Also, it seems to me, as we contemplate these things we must try to think of God's wondrous 'glory' characterized by His tremendous 'light' as indicated by scripture. I am sure no human can comprehend these fully, either. Moses, Isaiah, and even James, Peter, and John probably had a degree of comprehension given their experiences, some more than others. I think scripture indicates this 'light' is blinding to fallen eyes and required God's assistance to men even in the biblical examples. To me, nothing is more awe-inspiring than the light and glory of God as they are characteristics of His holiness and His beauty.
Fascinating as it all is, I agree that God's manifestations, however they may occur, can only be 'glimpsed', at best, by fallen man and are beyond our comprehension just as His holiness cannot be comprehended. Right this moment I feel like a 6 month old baby in front of a classroom trying to give a lecture on quantum physics.
