How can I copy and paste a Facebook account link on iPhone using iOS 8.0.2?
If you are using Safari, there are known issues with the Copy & Paste function in iOS 8.
But basically, navigate to the profile page, at the top tap in the address bar, select all, then select to copy. Now, tap where you want to paste it to and select paste (all assuming it doesn't bug out).
Not sure about the FB App, not a FB user therefor never used it.