About the family: As far as I remember, there is nothing in the WT's regulations that says someone like 'T' cant visit/talk to her family members, regardless of their religious beliefs. Even if they're disfellowshipped they can still talk to them (although many get carried away by their emotions and righteous indignation and choose to 'shun' anyway). Although the WT might slip in a little suggestion to be 'mindful' when in the company of worldly family members, I dont recall them ever ordering people(offcially at least) to break off contact with family members. I think the strongest thing they counselled was to keep 'associations to a minimum' with disfellowshipped family members. If they relatives have never been disfellowshipped, and are part of a Baptist church, the witnesses in the KH might encourage contact with them, so that they can 'bring them the truth', who knows?
About worldly friends: When I was a JW worldly friends were vehemently discouraged, so much so that I started to view non-jws as almost sub-human. FB wasnt around when I was in the 'troooth', but chatting to and becoming friendly with worldly people on the internet was just as strongly looked down upon as making friends with co-workers, classmates, etc. On top of that though, I think association with worldly people of the opposite sex was even more taboo, because of the fornicatory reasons that jws love to dwell obsessively on night and day. So what she's saying to you might not be much of a deviation from what you'll find in mainstream jw thinking(twisted in logic as it is).
About the mother: She's got worldly friends on FB because, let's face it, you hardly ever have any contact with 90% of the people on facebook anyway, and they are often little more than a photo album and a sentence or two posted next to their name, if anything. I'm sure that'll be her reasoning, that they arent 'real' friends, so it doesnt matter. She's being naughty though, she's not listening to the WT, cause the WT actively discourages socialising with non-jw friends, as I mentioned before.
What you MIGHT find, is that if an Elder, or Elder's wife that she respects, was to highlight this in a critical way, or if this came up in a very damning talk from a CO, that she might suddenly choose to delete all those friends....It would be unlikely that she would give a toss if you pointed this out to her, cause you're just a worldly little nobody in her eyes, what do you know....?
long story short = no, they shouldnt be having worldly friends on FB, but more importantly, should YOU be considering ending YOUR association with 'T' if it looks like she's going down the fundamentalist road...? What exactly would you have in common anyway? Trust me, its difficult maintaining a friendship inspite of the WT brainwashing, I know, i've been there(except I was the brainwashed person). If she gets deeper and deeper into the JW mindset, accept that(for the moment at least) your friend is gone, and take several steps back. You never know, she might come round later in life, and you can be mates again...