I'd love to know HOW she is doing it at all. Before I came here to marry my husband and stay, we spent 3 years travelling back and forth across the Atlantic visiting each other for vacations. During my visits here we did a lot of travelling, one time we drove up the West Coast from San Diego to Bellingham and all points in between (fantastic trip) and had originally planned to go over the border into Canada for a couple of days before heading back to SF only to find out I couldn't on my British Passport. Well, I could go into Canada BUT I wouldn't be allowed back into the USA, same with Mexico on another occasion. Something about the visa waiver program, you can only travel into the USA from your country of origin (unless you're making a stop to change planes en route of course)you have to apply in advance to the US Embassy for temporary visas to cover any short border crossings.
As far as the SS# is concerned for alien residents, this is issued very early during the Green Card application process. After you have sent in your applications USCIS send you an official letter which gives you your Alien Registration# and extends the 90 days period you can stay in the country until the Green Card is approved. You have to take this letter to the DSS and they issue you with a SS# and card. Just having a SS# does not entitle a resident Alien to work however. Even if you have applied for a temporary work permit at the same time as you applied for the Green Card (as I did) that still takes a couple of months to be approved and come through.
Oh yeah (not sure if this has already been answered - apologies if so) the passport style photos? Yes, the Alien has to send in four to USCIS with the Green Card application and the sponsor ALSO has to send in two of themselves. They also have to be endorsed and signed on the back by some respectable member of society who knows you.