The simple answer is "Yes," "Yes" and "Neither!"
Jesus taught us that God is spirit and humans do not have sufficient knowledge to definitively say that "human gender" applies in the spiritual world.
God exhibits all the characteristics of person-hood: God has a mind, a will, an intellect, and emotions. God communicates and He has relationships, and God’s personal actions are evidenced throughout Scripture.
So, what does God teach us about himself?
Throughout the pages of Scripture, God refers to himself and reveals himself in the male form, specifically as in the person of Jesus, but does this make God only and fully male?
In the Book of Genesis, God says:
"Let us make man in our image, in our likeness, and let them rule over the fish of the sea and the birds of the air, over the livestock, over all the earth, and over all the creatures that move along the ground." So God created man in his own image, in the image of God he created him; male and female he created them."
In these verses we see the reference to the pre-incarnate person of Jesus, as in "Let us make man in our image" and the Oneness of God where we read "...he created him; male and female he created them."
If we are truly made in the image of God, then God's 'image' is revealed in both the male and the female. The following is an excerpt from www.gotquestions.org:
"Both man and woman are created in the image of God, in that they are greater than all the other creations as they, like God, have a mind, will, intellect, emotions, and moral capacity. Animals do not possess a moral capacity and do not possess an immaterial component like humanity does. The image of God is the spiritual component that humanity alone possesses. God created humanity to have a relationship with Him. Humanity is the only creation designed for that purpose."
The following books deal with the subject of the person of God:
The Shack has sold more than 10-million copies and is presently being translated into 30 different languages, yet it has stirred up some controversy. It is strongly recommended to view the following video of an interview with the author, William P. Young, so the book can be read in context.