I have my PS4 set up in my living room and just bought my friend's PS3 for my kids room so she can watch PS Vue. I tried changing the PSN email on the PS3 but it won't let me use my PSN email. Can I use my PSN account on multiple devices? If so, how do I do that? My friend didn't clear anything off the system so all her stuff is still on there, so I don't know if that could be causing the problem.
Yes, you should be able to use your PSN account on multiple devices. I'm personally using the same account on my PS3, PS4, and PS Vita. What is the specific error message you are seeing while setting your PSN account on the PS3?
If you haven't cleared out / logged out of the prior person's PSN account, that could be causing issues as well. Please see here for that: http://manuals.playstation.net/document/en/ps3/current/account/signin.html.