You don't have to harvest your crops, but why wouldn't you want to? You get money and your trees grow older/mature and get more fruit in the end.
I'm afraid not.
I've been playing for a while and I've not come across it. I don't think you can.
Go to the map in the bottom right hand corner and go to the Retail Office. It will automatically pop up a screen and you can choose to upgrade your farm.
Um.. no you cant. I have been playing farmtown for years, you cant sell it