"They rent my building" should also be correct.
Yes!
i think it is correct too but ...
Just to see if I get the difference between me- and me-kan verbs right: Would "saya menyewaKAN gedung saya" mean "i rent OUT my building"?
I'm also curious about the directional aspect of the parties involved in the rent. Is it reflected in the language in any way like in English?
Yes, absolutely correct. Saya menyewa ... i rent... Saya menyewakan .... i rent out Happy learning!
Is there a difference between "kos" and "menyewa"?