Mormons believe that God consists of 3 beings, united in purpose. They call this the Godhead.
The Mormon view of the three persons who make up the Godhead is that they are in fact 3 separate beings.
When Mormons speak of God as eternal they don't mean that God has always existed in the same form, but that God has lived for so long that it's impossible to imagine a time when God did not exist.
Since God has a body, he can only be in one place at a time.
Because he is a person he can only be in one place at a time, like God the Father and Jesus Christ. However the power and influence of the Holy Ghost are everywhere.
Mormons use an analogy with the sun to explain this.
The sun itself can be in only one place at a time. But the heat, light, and energy that radiate from it fill the entire solar system at once.
Similarly, the Holy Ghost as a person can be in only one place at one time, but his influence and power can and do fill the immensity of space.