What exactly goes on at sorority/fraternity date events?

Dates are choose usually by the person hosting the party. So if the fraternity is hosting the party the members of that fraternity invite who they would like to be their date.

Going to dinner and restaurant depends. My fraternity for our formals we had most of the partying at the house and we might go to a restaurant with a group of guys and our dates but some times we didn't even bother. Sometimes some brothers would get together and cook a nice meal at the house to try and impress their dates.

As for sleeping with your date that all depends on the two people and whether they mesh well. I have had formals where I just took a friend and there were no attempts for sex or anything. Being that for most of college I usually was in a relationship or had a girl I was seeing regularly and they were my date for the party We would have sex like we always did most weekend nights. Most college students if they are out partying are hoping to get lucky some how.

At the party part there was dancing, drinking games like beer pong, quarters, flip cup etc. Standard college party atmosphere.