I can see horses and poultry, but why would they bring cattle, pigs and sheep along? Maybe they'll pick up some pigs along the way from the Polynesians, but they are just as likely to eat them on the way. Remember this is a very long trip, and they don't plan to be pig farmers when they get there.
A Java expedition probably wont include any Koreans. The invasions of Japan was another story.
The other livestock would have been brought for dietary variety. They also would have probably replenished their stocks in Java. They would have eaten a good number of their animals, but not all of any one species I think.
They did not travel through Polynesia, so did not have a chance to pick up Polynesian pigs.
As cosmopolitan as the Yuan empire was, taking advantages of the skills and knowledge of the peoples they dominated, I expect that there would have been Koreans in the Fleet. They were masterful sailors and shipwrights.