Your view about an apostate is well known, but the Talmud apparently did not hold that way. “From where do we know that one may not hand a limb from a living animal to a Noahide? As it says: ‘And do not place a stumbling block before the blind.’”
You’ll say that the gentiles of old believed (in a commandment? in the Commanding One?) — yeah, right…

Jacob, there’s no need to say that the gentiles of old believed (both in the commandment and in the Commander), but rather that the prohibition applies only to such gentiles. But from the words of the medieval authorities, that it is forbidden to hand something to an apostate to idol worship, and in general from the laws that apply to such an apostate, it seems they really did not think that someone who wholeheartedly denies the Torah ultimately receives leniencies. To say that even an apostate to idol worship “knows his Master and intends to rebel against Him” is already a far-fetched fantasy. Just as all the nations believed in their abominations, so too that apostate presumably believed as they did.

You’re saying there is proof to forbid it from the medieval authorities, not from the Talmud.
But even regarding the Talmud’s statement, this is an interpretive setup with not a shred of proof.

Rabbi Michael Abraham is formally bound by the Talmud, including the baraitot cited in it. According to his approach, he is not formally bound by the words of the medieval authorities, and substantive authority falls away if in his opinion there is a very strong rationale against what they say.
As for proof for the interpretive setup, as you put it — well, come and see what kinds of interpretive setups the Talmud makes in the Mishnah, and what kinds of interpretive setups the medieval authorities make in the Talmud.

It all depends on how strong the learner finds the reasoning that rebellion against the command is critical to a transgression, and obedience to the command is critical to a commandment. And this is a general issue in the conception of transgression, and apparently also depends on the laws of an unintentional sinner, one merely occupied with something else, and one acting under coercion (whether from an external force or because his heart compelled him).

By the way, although Rabbi Michael Abraham himself holds that in these interpretive setups the interpreters tried to hit upon the intention of the earlier source whose words they were reinterpreting — the Talmud regarding the Torah, and the medieval authorities in turn regarding the Talmud — there are other views as well. Strange as they are from the standpoint of truth, they maintain that some interpretive setups are actually a subtle disagreement with the earlier source when needed, and that they used a forced reinterpretation instead of an open disagreement only so as not to break the constraints of the written text, because that would create problems, or because the text has substantive authority. According to those other views, the leash has really been let loose.

Well, let’s say that this reasoning too — to permit causing a secular Jew to sin — is not exactly convincing.
And does this “permission” apply also to moral commandments and moral transgressions, or only to religious ones?
(For moral commandments and transgressions, is intention/belief also required in order to be liable?)

Why isn’t it convincing? If someone is wholeheartedly certain that something is permitted, what is the Holy One, blessed be He, supposed to be angry at him for? You can’t expect anything else from him.

What moral transgression, for example?
If we’re talking about harming someone else, then indeed that must be prevented, or at least not assisted, regardless of intentions. There the issue is not what is demanded of the person in deciding correctly; the goal is that the harm not occur.