If we ignore the first pamphlet, the only definition that comes out is self-cause.
And there are three main actions that He performed: designing the world for the creation of complex human beings, legislating morality, and giving the Torah. But all of those are actions, not a definition. So all that remains is only self-cause.
Does the God of the pamphlets have consciousness? Does He have free choice? Is He personal? Isn't it a bit too Christian an approach to say that He can be happy?

First, there is a need to define the concept of God, but there is no need at all to define God Himself or to know Him. Every argument proves the existence of a being defined within its own framework. Thus the ontological proof proves the existence of the perfect being (and not self-cause), and there is no need at all to know whether He has consciousness or choice. The same applies to the cosmological proof, which proves the existence of a being that created the world. Why is it important what His other characteristics are? If I prove that there is a president of the United States, is the proof flawed if I do not know his personality or the color of his skin?

Agreed, but I do not necessarily mean the partial definition of that being in that specific subsection of the cosmological proof, whether in the Kalam approach of a being that is self-caused, or in Taylor's style of necessary existence that is not contingent.
Rather, I meant how you understand the concept as a whole, in order to know what the overall discussion revolves around.
Does this being have consciousness or free choice? Is it the God of the philosophers, who acts necessarily, so that our prayers too operate according to criteria of improvement, intention, and so on—or is it rather out of will?

From the “but” in your words there seems to be criticism of a discussion that does not define its concepts, and therefore I wrote that this criticism is not justified. As for the matter itself, it is difficult to speak about His attributes. What does “consciousness” mean in His context? Like ours? I do not see how that can be answered. As for freedom—in my view it is reasonable to assume that He has free choice, but on this matter too it is hard to be decisive. (In my latest column I brought Rabbi Kook's remarks on this issue.)

Not like ours, but not like a stone either. I mean that He is more “warm” than a cold entity like a stone.
Yes, I actually saw the post where you quoted Rabbi Kook. But isn't that a novelty? I have not come across anyone claiming that He really has free choice—other than Christians, from whom it sounds like God is very personal…….
Usually in Judaism people speak about an primordial will that does not change (because otherwise there is a problem of perfection), but that feels a bit different from Rabbi Kook's words. And especially since you hold that He has no knowledge because we have choice. It sounds like you are more able to accept a newly arising will.
If He does not have free choice, then according to your view does He not require sufficient reason?

This question came to me because not long ago I heard a lecture by one of the modern thinkers (about whom my teachers told me: in their audience, keep quiet), and there he used very freely expressions that are very human when speaking about God, like joy, delight, and so on—expressions that, truth be told, I do not remember ever hearing before.
And when I asked him at the end of the lecture about the fact that Maimonides would not have spoken that way, he told me to interpret his words with qualifications, the way Maimonides himself did.
But the “small” difference is that Maimonides shifted the attributes into attributes of action, whereas he uses them as attributes of the divine essence itself, may He be blessed.
And therefore I am very interested in your opinion on the subject, because before I heard him I had barely thought about this issue.

It does not seem like a novelty to me. When people speak of His will, they plainly do not mean a mechanical will.
But as I said, these discussions are, in my opinion, of no value. No one can really answer them, and it is not clear whether they even have a clear meaning.