Kiranga,
Asking about where intelligent of God came from is very stumpy but of course is the better way to try to clash and escape but lets go through it a bit. Nisamehe tu kama nimeingilia but I guess you are okay with it.
If intelligence must come from intelligence, where did gids intelligence come from?
You mean God I suppose, we believe God is forever existed intelligent or for your satisfaction his intelligent came from thyself. I have used word "believe" because that where we stand for just like you could have say you theorize about big bang or multiuniverse etc.
Which intelligence gave rise to god's intelligence?
Answered above I suppose. Let me avoid repetition
And if god's intelligence was caused by some external factor, is that god really a god or just a highly complex being?
Not from external source. He is the source. And by the way does it matter if God is highly complex being or "really God"? What is the meaning of the two for you? Whatever he is it doesn't take away our definition that it is God since that is what we as humans identify him on whatever he is either a force or being or beam of light (no one has seen him) but the most important for us he is conscious and has personality. He has personality that is why he created the universe for a purpose, anything that has a purpose then has a personality.
And if god did not get his intelligence from an external factor, is it really true that intelligence must come from intelligence?
Yes it is but for him it is "exceptional circumstances".
Kiranga, I think you recognize that even in science there are exceptions and some physics laws and others might not work out the same in other complex environment. For example in subatomic world, or even in the middle of the black hole. In subatomic world, the smallest particles behave totally different from the laws of physics that we know and take for granted in normal context. For example the observer-effect; when the particle changes when they are observed, and the particles can be at two different places at the same time. That means when comes to the subatomic world many laws including the law of gravity totally breaks down.
In the center of the black hole basic laws of physics guiding the arrangement of matter is clashed and even the gravity fails and light cannot come out. Isnt it?
Now you tell me why there is exceptional in subatomic world where the physics laws on normal circumstance do not apply? If they would we would have been having one person being at the two different places at the same, well electrons does it, photons does it…
Then you should explain to me why you set your questions and assumptions based on the limited nature of the same world we are in? You should realize God is above that? He is not bound by our physics laws, he is far greater than that, (Remember there is exceptional circumstances huh?) Even string theory suggests extra dimensions than the ones we know, more than 13 and lets not go there, strange things are suggested mathematically to happen in string theory not even single law of normal world would apply.
The concept of something must be created by something has limits, We shouldn't assume through only our levels of knowing and maybe experience (and according to the laws that apply to us), but for God all those laws work totally differently. He set the laws. The tiny part of knowledge which is start to be revealed scientists that there are exceptions which they didn't know, is the sign that the power above is far greater and is not bounded by general relativity, strings theory or super symmetry theory.
Thanks