My parents are flying in from Mexico City to Tijuana I would like them to use the CBX can I purchase their pass online and have them print it before their flight?

I think so. I have done it that way before

You can purchase the tickets at our website www.crossborderxpress.com, you will get a confirmation email with an attached PDF with your e-ticket(s) you can print it out or scan it at our e-gates directly from a cell phone.

Yes you can. And if your parents are like mine, they might prefer the printed version.

Yes

Yes, you can just send them the pdf of the tickets to their email and they can use their phones to scan the code

Yes you can

Yes you can also picture text them the tickets.. when they pick up their luggage it be the 1st line they see.. make sure they go through that line that says CBX