Are the arguments for the belief in God based on logical fallacies?

The issue of unable is different from the issue of a god. I'll deal first with the question of God.

The God Issue

Before we can discuss whether something exists, we need to know what “it” is. We need a specific definition to make sure we are all talking about the same thing. In the current discussion, I understand you to be making the proposition: God exists.

In logic, as in law, the proponent of a proposition must present (1) an intelligible definition of the god and then (2) bear the burden to adduce evidence to support its existence. No one has ever presented me with (1), so we never got to (2). 

By “intelligible definition,” I mean to state or describe (with sufficient specificity to be clearly understood by all participants in the discussion), the properties (i.e., the attributes, qualities or features regarded as a fundamental, characteristic or inherent part) of the god under discussion, which properties are not internally contradictory, not in conflict with other properties or attributes ascribed to the god and which distinguishes the god from other gods or entities.

 Note: I understand The difference between attributes and properties is subtle. Properties describe the characteristics of an object and attributes refer to additional information of an object. Most people use these two words as synonyms, and that is acceptable to me.

The problem faced by those who profess a belief in a god is not they cannot adduce any evidence to support their belief, but they cannot even specify what it is in which they claim to believe. 

For example (to borrow from Branden), the man who claims to have faith that he will win at cards can at least define what it is in which he has faith — in the sense that he knows what he means by winning at cards. But if he claims that he has faith in a god, he cannot, in any like sense, specify what he means. He can identify his god, in effect, only as a feeling, he has faith in a feeling. But since faith is only the worship of feelings, the man who declares to have faith in a god is declaring that he has a feeling about a feeling—restated a feeling that his feeling is true. Thus, faith in an undefined god is mysticism two times over. It is an act of faith twice compounded.

I doubt the person proposing the existence of a god believes in the existence of Zeus, Thor or any of the myriad of ancient Egyptian gods. By definition, as to those gods, that person is an atheist. As Richard Dawkins says, “We are all atheists about most of the gods that societies have ever believed. Some of us just go one God further.”

Unknowable vs Unknown

To be unknowable is different from unknown. Unknown merely means something not known at present or not known to you. But unknowable means that which can never be known. Unknowable is that which, by its nature, cannot be known. 

Many people proffer the proposition: God is unknowable. Their first hurdle is to define God. Beyond that, they must explain how do they know God is unknowable? To do this, they already know something about the god: it is unknowable. Yet to know something about the god is to have knowledge, and that alone contradicts the proposition. Beyond that, they have to adduce evidence to support the proposition. The old Burden of Proof rule rears its reasonable head again.

I would say it cannot be proven or not proven that God exist.

""why are there stars in the sky?" - then it is unknowable and therefore it is only because of God" is just an assumption or maybe an argument from silence.

But another we hear a lot is that if you can't explain some aspect of life - "why are there stars in the sky?" - then it is unknowable and therefore it is only because of God.

This line of reasoning is very common, even outside of the 'God Debate' and wider theology. It is fallacious.

Logical form:

You posit theory A, to explain some phenomenon P.

I posit theory B, to explain the same phenomenon.

Assume either A or B (but not both).

Not A (your theory is wrong).

Therefore, B (my theory must be right).

This is a False Correlative - specifically, Denying a Conjunct. Because one theory is falsified or disproved, the speaker infers that their theory must be correct, without reason or evidence, and this ignores the possibility that both theories are wrong. It is a form of Privileging the Hypothesis, in which there is no solid advantage to one explanation over another, but because the speaker is biased, they claim that their explanation is correct - for instance, although theory A may now be known to be wrong, there could be other theories, and without evidence, only biased reasoning would lead one to accept B.

If the theories are mutually exclusive, then they are independent of each other and require their own bodies of evidence. One falsified explanation says nothing about the truth or validity of the others.

Your calling out of the Confusing Currently Unexplained with Unexplainable is also accurate.

You might want to be careful with your title which is too broad to then summarise as the god of the gaps argument, even if that's what many arguments boil down to,  not all of them do.

The god of the gaps could be referred to as an argument from ignorance, or a subset of that which is an argument from personal incredulity, or it could be referred to as an ad hoc rescue.

It takes the form of "we can't explain X, therefore we can arbitrarily insert "god" as an explanation". Last time I checked if you can't explain something then you can't explain it, and just claiming an explanation, which isn't an explanation anyway, is a contradiction.