"*In the "what if an ax murderer asks me where my friend is, shouldn't
I lie then" the obvious solution is to just remain silent. I'm
thinking of cases where there is no similar way out, e.g., you are
This is wrong. There's no "obvious solution", as though it were a logical exercise. Kant's point is you don't know, with certainty, if the guy is going to catch him. He says, maybe the guy will have already slipped away. And then your lie didn't help at all, might even harm the guy. One should read, here, the example Dostoevsky gives in the Idiot, about the injustice of State execution. Saying, the state is far more cruel, since in the case of a knife murderer (likely he thought of Kant), one, till the last, thinks of escape. Whereas, in the execution, the State's iron laws work evil like clockwork.
If you lie, then a judge is supposed to ask, did he really aim at not lying? It's a causuistry. You must faithfully interpret your duty into the situation.
In other words, not lying is a predelineation of the ought, it's what would happen in a perfect world, in the sense of if one ought to one can. If one ought to one can means that the way the world is, practically, in reality, need not always be. One might, through habit, bring about the world where one need never lie. He aims at a Utopia. But, he knows this is not Utopia. Kant's practicality is vastly effaced by the false reception of his thought currently on the market.
Thusly, rethink your question.
Also, be sure to remember
"we are prohibited from using people as purely means"
does not preclude "doing violence onto you just because you don't want to be wounded" which "seems to very much be using them as a means and not an end."
Since using someone simply as a means, is not the same as partially doing so. Otherwise one couldn't use a hatcheck girl to get one's hat.
we are unable to escape being submitted to unethical treatment. This seems like a difficult to sustain interpretation of Kant (even building on the formula of humanity).