I communicate with a girl's father (they live in the "end of the world"). There is no direct contact with her; everything goes through the Wali. He informs her about our conversations and occasionally sends me her answers to my questions and information about her. Is this permissible? Where Borders?

Yes, this is permissible. You can even talk to her on her father's phone while her father is there and listening to every word. This is allowed, but don't push it too much. You can talk a little bit so that you can decide if you're going to visit or not, or if the marriage is going to proceed, and so on. But to make it a kind of distant relationship is copying the disbelievers; this is not a healthy way for a marriage.