You cannot get $_POST where you are trying to do it. When the ACF form is submitting, the form is process and then redirected back to the page. This means that when the page reloads $_POST will contain nothing.
Similarly, you cannot display information during during acf/save_post, once ACF is finished the page is redirected, so if anything is displayed it would be removed when the page reloads.
You need to use acf/save_post, but you need to do something with the information other than display it. This is where you should be sending the data to the other API instead of trying to display it.
