I was wondering if it is possible to get custom emails for my GitHub pages site (for example: firstname.lastname@example.org rather then email@example.com). If you know how to do so, please let me know.
Yes, it is possible but not through GitHub. You would have to contact a service provider for email like Google Apps or FastMail. Whichever service you choose would be able to help you through the setup process.
I hope that helps!
There is a choice of solutions for that, paid and free, and indeed all of these happen outside of github. On the free side here are a few free services:
Zoho Mail free plan limits you to their webmail only, and Yandex has ads. postale.io doesn’t have those limitations. The DNS setup is also taken care of for you, if requested (still for free).
Hope this helps!