Mostly agree, but I'm not sure that he's "changed" a proof into a definition. The "proof" itself is already largely a definition: we call the "first cause" or "prime mover" "God."

Everything has or had a cause.
The universe is a thing like everything else.
Therefore, the universe has or had a cause.

As you, the conclusion tells us nothing about the presumably necessary cause of the universe, except that it caused the universe.

Any additional characteristics we might add are baseless, at least on the basis of this syllogism.

And the syllogism, while deductively valid, may not be sound. Do we know that everything (the universe included) has or had a cause? Quantum physics, developed centuries after the syllogism, strongly suggests that certain existing "effects" have no cause.

What if the creation of the universe (from a "singularity") was more like a quantum effect than like, say, a person making a watch?

And what if the "universe" (which now presumably includes an infinite number of parallel universes) has existed eternally?

People often as, "Why should there by something rather than nothing?"
Good question. But, alternatively, "Why should there be nothing instead of something?"

After all, everything we see or know is about *something." Since "nothing" has to be defined as the absence of all possible things, doesn't that suggest that "something" is the norm and "nothing" the exception?

Suggesting it, of course, hardly makes it so. But it's an interesting point.