How to set up cash payment along with PayPal option?

Then after the online payment is validate or if the user check the box pay cash, he must receipt with e-mail also

It is possible to have 2 payment options, PayPal and cash, on the form. You would need to create a field, which is asking if user would like to pay by Cash or PayPal. Then, based on the answer, PayPal field can be shown or hidden. If Cash option is selected, user will be able to submit a form without processing a payment and submission will be counted as completed, email will be sent out to the user. 

Please review the following detailed guide: How-to-Set-up-PayPal-Along-with-Other-Payment-Options