You are absolutely correct in being cautious, and as Miccah said on sites such as Facebook you can set your privacy to friends only, but even then people accept friend invitations from people they have never met, for me only friends that I know personally have access and my two teens do the same.
Some sites though don't have these restrictions and are open to the public and mistakes are made by us all.
You should never give your full name - full date of birth- just either the day or the year never both together and never give your address. Identity theft is a problem fast on the increase and we have to be wise and take steps to protect ourselves.
When placing photos on the web be careful that you don't show door numbers, landmarks that could pinpoint your house and names of schools along with childrens names. Paedophiles are known to approach children using their name, these children are then confused because this stranger must know them, because they know their name and maybe even the mum's name.
You also are supposed to ask permission of any person who appears on photos if they mind you uploading the picture.
I don't know about America but in Britain you can be sued under the data protection act for giving out another person's personal information, now even if a friend asks me for someones phone number I will ask the person wanted to ring them back with it!
It is surprising how much information we do volunteer about ourselves that if we are not wise can be used by the wrong people.
I was shocked once when just messing about I did a google search of my name to find sites that had copied my testimony that I'd written out for a lady!
The sites to be very aware of are open chat rooms and on-line gaming, these are a playing field for paedophile activity and people can be someone they are not, even my husband has had men coming onto him thinking he's a young woman! If they go too far he will report them, you have to stay close and monitor children who go on these. My husband sat with our daughter and was horrified at how quickly the questioning by people online turned dangerous, as soon as she mentioned her dad was with her they immediately went off line - it goes to show you cannot trust everyone online!
We tell our children not to talk to strangers and then let them do exactly that while sitting in the comfort of their own home, which lulls them into a false sense of security and everyone is their 'friend'!
I would recommend that you obtain leaflets from your local police on internet safety guidelines, also I would strongly recommend the 'Churches child protection advisory service' known as C.C.P.A.S They have a new leaflet of advice for parents.
C.C.P.A.S have a website you can check out and information that you can view on line. This site is run by dedicated Christian staff.
I hope this helps and please advise your family to think about what she is doing, we always have to be on guard.