Here’s what Dei Verbum says. It seems relevant to your questions.
God, who through the Word creates all things (see John 1:3) and keeps them in existence, gives men an enduring witness to Himself in created realities (see Rom. 1:19-20). DV3
As a sacred synod has affirmed, God, the beginning and end of all things, can be known with certainty from created reality by the light of human reason (see Rom. 1:20); but teaches that it is through His revelation that those religious truths which are by their nature accessible to human reason can be known by all men with ease, with solid certitude and with no trace of error, even in this present state of the human race. DV6
Using DV as a guide, I would respond:
a) Is a distinction able to be made between rational and irrational faith? (i.e. Is belief in Zeus irrational and belief in Christ rational?)
It is irrational to fail to address the question of who or what is the Originator of all things, including the Originator, or Creator, of the various gods of mythology. To the extent that other cultures acknowledge a Creator, though they may also have erroneous concepts attached to that belief, they are on the right track in satisfying the demands of reason. Yet, as DV says, it is only by divine revelation that the errors can be removed.
b) Is belief in a benevolent god more reasonable than in one who is indifferent (deism) or even malevolent? If so, how? (Please be explicit.)
Of course, having already been influenced by divine revelation, my starting point assumes that God is indeed benevolent, and that even those who do not have the benefit of divine revelation can deduce as much from observation of created reality. How? I suspect this plays out in highly individualistic ways. Yet one might reasonably conclude the Creator’s benevolence by comparing that which we absolutely need in order to live, with that which exists in the beauty and vastness of the created world. In other words, could not humankind exist without the beauty of the ocean; the Grand Canyon; another person, etc… Would life not still exist if food was simply a means to nourishment and not truly enjoyable? Couldn’t the same be said for sexual pleasure?
The benevolence of the Creator can be reasonably deduced by the superabundance of gifts the He created.
c) Is it less reasonable to believe that one shall be rewarded (in the afterlife, of course) for the murdering of babies rather than the feeding of the poor? If so, how? (Please be explicit.)
Human experience even amongst the most primitives indicates that actions bring about consequence. Not just in the physical sense, but in the realm of human relationship and human emotion. The killer and the dictator can seem to enjoy reward on earth, but the repurcussions they engender; fear, hatred, etc. are discernable by the light of human reason, and this indicates that certain actions result in the opposite of reward. The natural law makes known the norms of right and wrong, even as sin clouds our vision and wounds our ability to reason.
d) By what criteria are theological claims judged?
In context with your other questions, I would say that one criteria is that authentic matters of faith are never opposed to reason. In fact, truth naturally appeals to human reason.
I believe it is difficult to remove from one’s own experience the benefit we enjoy of divine revelation when seeking very specific ways in which reason alone allows us to know God. I also think, as I said, that the specific ways in which God makes Himself known often manifests in very personal ways among individuals.