here are some answers to your ?'s. . .
1) i have no experiance with this as my parents aren't divorced, and they pay for the sorority. sorry
2)our formals are sorta like dances, like you get all decked out and stuff. finding a date is usually no problem. the girls do the askings to sorority functions and the guys do the askings for fraternity functions. if you have a guy friend take him. if you don't, your sisters will know plenty of people. guys don't like to admit it but they love coming to sorority functions!
3)i didn't know anyone in a sorority on my campus. i rushed (it was rush went i went through!) first semester my freshman year. i went to high school overseas, so none of my friends went to penn state with me. . .i don't think it hurts you if you know someone either. just make sure you're rushing their sorority for the other girls too, not just the one you know.
4)i think researching the sororities before hand is a good idea. you can usually kinda get a feel for what they do on and off campus by their websites.
5)i might mention it if the topic came up. i don't think it would hurt. our philanthropy is alzheimer's and i know that some of the girls i rushed mentioned that they had a family member with the disease or had worked with alzhiemer's patients before. i wouldn't invent something to make is sound like you're really into the sorority's philanthropy to get a bid.
some other advice is and you'll hear it time and time again JUST BE YOURSELF!!! good luck! let us know where you end up!