Tracking Opens

There is nothing in Acrobat that would allow this out of the box. You can add custom JavaScript that "phones home" to count how often the file was e.g. opened, but the user has to agree to open such a connection. Take a look here for some inspiration about how to do that: http://khkonsulting.com/2017/08/connect-database-pdf-form-time-without-soap/  and http://khkonsulting.com/2016/06/getting-serial-number-form-using-soap/

These articles are about a different use case, but there is no need to display anything in your PDF file, you can just use the same methods to increment a counter on the server. 

Again, the user has to agree to let you open a network connection.