If I do not friend someone on facebook can they message me or see anything on my facebook?

[carmen]

[T]

Go onto your timeline.
Click settings (right from your profile picture).
Then click view as.

This will show what it looks like for the public.
You can change the settings to more private if it is not already.

[Md Melon]

Go on your timeline.
Click settings
Then click view as.

[withaC]

A> Someone [non-friend] being able to message you on Facebook all depends on YOUR privacy settings.

B> Click the lock at the top right of any Facebook page (review your Privacy Shortcuts).

C> Also, go to your Timeline and Tagging Settings; go to Who can see things on my timeline?

[Angeleyes]

It depends on your settings, if you don't want anyone to see anything change your settings to "only me" or 'friends only", also check the strict filtering for who can message you. If all fails just block them.