Yes. You can use Messenger using a mobile phone number. Just tap the "Not on Facebook?" button.
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No not really. Messenger is an independent app, you can work with it even when you dont have facebook app.
Facebook messenger does have some security issues that have people concerned but other use it and say they have no problems using it and are not concerned about it.
I have facebook mobile and you dont use internet its all texts
use a proper facebook messenger, it's better plus has more features. use this http://www.facebook.com/apps/application.php?id=102332746051&sk=info you can be invisible while still seeing who is online. And be online to some friends, while appearing offline to others. Also has a cool away/busy function.
By texting them using their cellphone. They can also use a program like Textfree or Yahoo Messenger to send messages to people on Facebook while not on Facebook.