Friends can help with a mission one time per day, and help a total of 5 friends per day. The missions are unlocked sequentially, so you have to rescue the teacup pig before you can continue to the next mission. In addition, you can only post to your wall once every 8 hours (which is a limitation by Facebook's Terms of Service). The missions also have a time limit - the Teacup Pig mission has to be completed within 7 days or you will have to start over.
So far, we're not impressed by these "missions". They are nothing more than wall postings to require clicks from friends - which is a tired mechanic that we're seeing all too often in these games. Perhaps you disagree and enjoy the Zoo World missions?