There are Facebook sites dedicated to people playing the game and introducing new friends, I was playing the game with no friends just to see how I could do, but when I went over 2.5 million, I decided it was time for friends and picked up close to 90 in less than a day! Good luck and happy building
That would be nice, but from a programing perspective its not possible. Your friends are part of your Facebook account and EA has no way of writing to your Facebook account. It's better to join a group if you are looking for friends to play the game with.