3 (a) “Existence depends on Consciousness” is a true statement; but (b) “existence depends on consciousness” is a false statement.
Why is (a) a true statement? I don't think it's accepted in Objectivist circles that the concept of existence depends on the concept of consciousness. I think Ed clarified this already. We don't need a concept of consciousness to have a concept of existence. Rand said as much in her Intro to Objectivist Epistemology. IIRC, she asserted that we don't develop a concept of consciousness till much later after we've already developed a concept of existence.
But if Existence means “existence”, and Consciousness mean “consciousness”, both statements 3 (a) and (b) should be true, because the respective terms have the same meaning.
First, (a) is making an epistemic claim. (b) is making a metaphysical claim. When we talk concepts we're usually focusing on epistemology. When we talk existents, we're usually focusing on metaphysics. So the contexts are different.
Second, it's been said before, but a concept is not its referrent. Just as the concept "red" is not itself red, the concept conciousness is not the same as the existent consciousness. The former refers to the latter, but is not itself the latter. This is how the quoted statements in (a) and (b) can both false. To be sure, you might've caused confusion by saying "the respective terms have the same meaning." (emphasis mine). In your scheme, "Consciousness" is a term, but "consciousness" is not a term; it is the thing to which the term "Consciousness" refers. They are not the same.
I think MSK clarified this already, but if it helps, I think Objectivists agree with the following:
1. The existence of concepts (any concept) depends on the existence of consciousness.
2a. Therefore, the concept existence depends on the existence of consciousness.
2b. Therefore, the concept of consciousness depends on the existence of consciousness.
3. the existence of consciousness depends on the existence of existence.
4. Therefore, the concept existence depends on the existence of existence.
Edited for spacing, which I can't seem to fix.