Hi Aliya,
Nope, there’s no DM or chat on Medium (not yet, at least). Just the comments section. One on one contact with writers must be done through their websites or social channels.
I think no DM is a good thing. This leads to thoughtful responses and allows everyone to learn from the answers that get posted. There’s plenty of DM-ing available on all the other platforms and it can get really overwhelming to keep up with.
-August