Oh yes, the new farm items are becoming more and more common by the hour. ( at first though it was funny. You could sell one potatoe for like 40 dollars. :) And to answer your other question the minecraft wiki holds your answer

 

Mhm, we all have auto farms for them, and to make a golden carrot, surround it in golden nuggets

 

It's wheat with a new texture.

Nothing exciting really.

 

Not as many growth stages, though. Wheat has 8. Carrots and potatoes have 4.