How to fix “App not installed. An existing package by the same name with a conflicting signature is already installed”

It means there are still some files from the old Facebook in your phone or you just already have the same app installed.

1) Reinstall the orignal Facebook/Messenger
2) Go in settings, then Applications manager
3) Go until your original Facebook/Messenger (pict.2)
4) Delete cache and Data (pict.4)
5) Uninstall your original apps
6) Restart your phone
7) Install The Hello Kitty Facebook/Messenger
8) Enjoy

If you have your facebook or messenger built-in, please check my post how to install a modded application.