Kant has been famous for his rejection of eudaimonism, but I think Kantian ethics has a great deal in common with Aristotle, and some things in common with Stoicism as well. The traditions tend, I believe, to talk past each other when it comes to happiness or eudaimonia.

Not only in order to act morally, but even to formulate theoretical questions, devise experiments, choose which ones to perform and what conclusions to draw from then - we must presuppose that we are free. That's the sense in which it is true that for Kant "we must assume we are free."

Kant was a rational theologian. He did not pretend to be a biblical or revealed theologian.

For the utilitarian, there is a fact of the matter about the good (the general happiness, or whatever conception of the good the utilitarian adopts) and about which actions or moral rules would contribute to maximizing the good. For the rational intuitionist, there are truths about which actions should be done and not done.

Fichte would identify all states of our minds with states of our body - perhaps not merely of our brain, but the whole body as an acting organism.

Kant's description of most ethical duties reads more like a description of moral virtues and vices. Once we see this, we see that Kantian ethics is indeed a kind of virtue ethics, and that it does not "divide the heart from the head" (to anticipate one of your later questions) but instead recognizes the deep truth that reason and emotion are not opposites.

It is absurd for anyone to think that Soviet "Marxism" is a correct application of the thought of Karl Marx. No doubt Soviet propaganda represented it this way. But who believes Soviet propaganda? It is remarkable (but maybe not so remarkable after all, when you consider their motives) that apologists for capitalism, who would not accept Soviet propaganda on any other point, are eager to agree with it on this point.