I am trying to figure something out for my mom. She receives emails whenever someone posts something on Facebook, and her only computing device is an iPad mini. She has no computer. She wants to be able to click on the link in Mail on her iPad and have it open in the Facebook app, not in safari. How does one do this?
There's no way, at the current time, to open links in anything other than Safari from iOS. Apple has not provided a way to set the default application for opening links, it's always Safari.
I'm assuming she's using the default Mail app (you didn't mention if she's. using a 3rd party app). One way might be to have her try a to tap and hold the link. This could bring up a share sheet. If Facebook is in that share sheet, she can tap Facebook to send the link to the Facebook app.
Another option is to you an app like Opener.
This app lets you open a copied URL in different applications but it's more of a work-around to the problem. You know your mom best, these additional steps might be more than she's willing/wants to do.