To start with, your "givens" are completely irrelevant to the point. They add nothing, they show nothing, nor do you reference them in any meaningful way.
You neglect case "A" in spite of it's philosophical implications. But I'll let this one slide.
You assume that cases "A,B, &C" are exhaustive. They aren't (that means you have not considered all possibilities).
Let us assume B. If the universe has always existed, then stars in the sky have been consuming resources for an amount of time equaling negative infinity.
"If the universe has always existed" DOES NOT imply "then stars in the sky have been consuming resources for an amount of time equaling negative infinity".
So your entire statement so far is an unsupported assertion.
Therefore not only are there no resources presently existing, there are negative infinity resources. We know this is false. Therefore Case B is false.
This is not a formal conclusion but another assertion as your initial premise was flawed. And clearly so. The primary star we know about is the Sun - it's a young star and it has not existed since the beginning of the Universe. Do you know how old our Sun is? Does the evidence of higher atomic number elements (lead, gold, etc) on our planet indicate anything to you?
Let us assume B again, only this time, we will go with the idea that resources will regenerate within stars via some reaction.
Why assume any such thing at all? We know about the life cycle of stars and I've never heard of anyone who suggests that they have been around forever, so you are arguing against a strawman.
So we know that stars have been shining in the direction of earth forever,
Again, this does not follow from the premise. If the universe has existed forever, or has gone through an endless cycle of Big Bang-Big Crunches, it does not mean that that any particular stars have existed forever.
therefore all stars in the universe, not concealed by phenomena such as nebulae, are visible from the Earth.
Even if we are in a steady-state, existing-forever universe with stars that "shine forever", we are still subject to the inverse-square law and atmospheric distortion, so no, they are not all visible from the Earth.
However we know also that a new stars light will occasionally reach earth,
True but irrelevant. Stars fluctuate in brightness due to a variety of causes, including age, mutual interference, and violent explosive deaths.
so Case B is again false.
So, we have bad premises, bad logic/leaps, and wrong (or, at least, totally unsupported) conclusions.
No need to proceed further.
Grade: F
I would hate to think that this represents the level your thought processes or your work in general.