Philosophy is about getting the facts right, but it is also about thinking rightly about them. Philosophy is more about the latter than the former.

We can never prove that we are free or integrate our freedom in any way into our objective conception of the causal order of nature.

No theory about our bodies as mere objects of observation and calculation (as distinct from partners in communicative interaction, assumed to be free) can comprehend human nature.

Kant does not think there is anything wrong with being beneficent from sympathy. He thinks we have a duty to cultivate sympathetic feelings by participating in the situations of others and acquiring an understanding of them. He thinks we also have a duty to make ourselves into the kind of person for whom the recognition that something is our duty would be a sufficient incentive to do it (if no other incentives were available to us). That's what he means by "the duty to act from the motive of duty".

Karl Marx left it to others to find the way beyond capitalism to a higher form of society. He saw his role as giving them as accurate a theory as he could of how capitalism works, which would also show them the reasons why it needs to be abolished and replaced by a freer and more human form of society.

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.

From the beginning, there has been a tension in the reception of the Kantian idea of autonomy. If you emphasize the 'nomos' (the law), then you get one picture: the objectivity of ethics. If you emphasize the 'autos' - the self - you get the idea that we make the law. Kant never hesitated in his choice between the two emphases. He emphasizes the nomos (the universal and objective validity of the law).