After the PayPal payment it redirects me to the my website. How can I set that user was redirected from the PayPal?
I did try the next variants:
request.env["HTTP_REFERER"]
request.referer
URI(request.referer).path
but nothing.
And one more question, can I catch that the referer is from PayPal exactly or user did it, the redirect, with the online tools, that was it fabricated or no?
This is exactly what PayPal's PDT feature is for. It sends you secure variables about the transaction just made, which you can verify via a postback to PayPal just like PayPal's aynchronous notification system IPN. Here's how:
https://developer.paypal.com/docs/classic/paypal-payments-standard/integration-guide/paymentdatatransfer/