As for the counters, you can use cookies.
As for the buttons, you can use links with get variable.
<a href='survey.php?survey_id=45&page=47&answer=yes'>Yes</a><a href='survey.php?survey_id=45&page=47&answer=no'>Yes</a>
And when the user visits, in other words-clicks yes,
<a href='survey.php?survey_id=45&page=47&answer=yes'> $_GET['answer'] gets processed, then the website refreshes to next survey survey.php?survey_id=45&page=48
In the database, it's better standard to use smallint(2) and put 0 as NO and 1 as YES.
And btw, your username is inappropriate.