How to send form values from the script in functions.php and not from the form on my website?

This isn’t really a wordpress issue and will probably get a better response be in the Stack Overflow PayPal page:
https://stackoverflow.com/questions/tagged/paypal

However, from what I’ve understood of your question, you want to know how to pass values from your form to PayPal?

To do this, you need to populate hidden fields and ‘send’ these to the PayPal address using the form post method.

The following link should help you out:
https://www.paypal.com/cgi-bin/webscr?cmd=p/pdn/howto_checkout-outside#methodtwo

If this isn’t what you’re looking for, tell us what conditions you wish to check for in your functions file and we may be able to help you further.