Quick reply
 

Hey!

Does the "quick reply" option work? I used it to reply to a private message, but my response doesn't appear in my "Sent" folder or anywhere else, so I'm not sure if it reached the person.

I'm not aware of anyone ever reporting problems with "quick reply" in our Private Message system.
Depending on default settings, it may not add the PM to your sent folder.

still the same
 

It's not only about 'quick reply'; my 'sent' folder is totally empty - it shows '0 messages', yet I've sent a message a few days ago and another one today. Just noticed it. Can someone take a look, please?

You won't see this option with "Quick Reply".
When sending a PM if you click on "Go Advanced", you will see additional options.
Then you have the option to select or de-select the option "Save a copy of this message in your Sent Items folder."