This strikes me as nitpicking. Not all premises need to be stated explicitly; all arguments have implicit premises.
Let's look again at the form of the argument as presented on the first page (and this is a criticism of William Craig rather than Tree of Life, since I know that the layout of the argument comes from Craig):
1. Whatever begins to exist has a cause.
2. The universe began to exist.
3. Therefore the universe has a cause.
If we were merely trying to demonstrate that the universe had a cause, this would be acceptable logic, but there is an implicit jump here all the way to a fully attributed concept of God. This is the way Craig sets up the argument: he explicitly argues for the two premises here, and then pulls a bait and switch and concludes that an immaterial, immensely powerful, personal, uncaused and eternal cause is the best candidate. I have seen him do this, and it's not nitpicking to say that this is
too much, too fast. I do not condone skipping steps of this magnitude.
Does it really need to be explicitly stated that God is defined as the creator of the universe? Is anyone confused on that point?
Honestly, that would be a terribly vague definition. We might as well get really tautological, define God as "cause of the universe," and ignore the question of whether this means that God will turn out to be a subatomic particle.
I don't like the Kalam, but the strength or weakness of the argument will derive from the defense of the premises. For example, what is meant by terms such as "universe" and "cause"? Is the creation thought to be ex nihilo? Judging the argument without sorting out these questions is too quick.
I disagree. If an argument is not valid, then there is no point in determining whether or not it is sound. If someone wants to simply demonstrate that the universe has a cause, then we could look at the premises. But if their conclusion is that God exists, then we can cry foul immediately, because even if the premises are correct, the logic doesn't get us to the declared conclusion.
There is nothing wrong with arguments that don't get all the way to God. I like PSR, for example, but I don't think it gets us to theism. That's fine, as long as someone doesn't tack on, "Therefore, God exists" at the end. I get tired of having to explicitly state that I'm not trying to get all the way to the theistic conclusion whenever I discuss a cosmological argument because people have been trained to expect the bait and switch.
And as I said earlier, a posteriori arguments for the existence of God all run up against the fact that the conclusion will not terminate in a full, classical conception of God's essence. Each argument indicates only one variable or aspect of that nature. In this case the attempted attribute is creator/cause.
If this were a classical argument, and limited itself to the attempted demonstration of one attribute, then I would not have a problem with it. (Or at least, I would not have this particular problem with it.)
William Craig is not a classical theist, however. He doesn't argue like a Thomist, one attribute at a time. This is very much intended to be a full abductive argument for the existence of God, and should be treated as such. I think you might have a blind spot here because of your Catholicism--the rest of us were taught to think in abductive terms rather than in demonstrating attributes. The universe needs a cause, therefore the best bet is that this magical entity we call God exists.
We're not being difficult, and we're not nitpicking. It's a really obvious non sequitur, and it poisons everything. There's a reason the first Christian I took seriously was Kierkegaard, and even after that, my relationship with natural theology was a trainwreck for years because of how arbitrary the whole intellectual tradition used to seem. This is a genuine problem in apologetics.