I've now realized that I don't know how to access to my old chats.
How do I know if someone answered me in a chat? Because I don't get any notifications in the "inbox". Is there a way to see the list of all the chats I've taken part in?
There are several things you can see there:
&page=2; similarly for more pages. (In your case, the second page is empty at the moment - if you post something more there, you'll see more messages. You can also see recent messages by other users, if you find them from the users tab.)