Since you don't have any code I am not 100% sure how you are going about most things but I can still give suggestions.
For your first problem, you could use $_SERVER['REMOTE_ADDR']
to get the user's unique IP Address and the time they are using your script using $_SERVER['REQUEST_TIME']
Like this
$uniqueName = $_SERVER['REMOTE_ADDR'] . "_" . $_SERVER['REQUEST_TIME'];
As for the other problem you can just save the variables in the session
so you can recall them anytime after you call the script. You could also use ajax
to asynchronously call the script that created the image and then using jquery
to populate the chart underneath it using the info from the form while at the same time removing form from the page.