Well, you can't get more farms... but you can make your current farm bigger! All you have too do is go to the upgrade section under the market, and then under that go to farm size! It's expensive but worth it (except for the massive o' farm)! You can upgrade sizes three times.
Attack other farms.
The one in zombie farm
At level 21
There are 5 different kinds. You'll unlock them on level 4, 8, 15, and 25.
Level up
you need a blue gravestone.
plant alot it depends on what level ur at
you buy it with real money. to buy it you go on choose your farmer and tap the king zombie head and it will take you to the app store so you can but it.
As you reach a level to unlock it, you can unlock higher level mausoleums via brains Mausoleum 2 - 3Brains needed Mausoleum 3 - 3Braines needed as well. not sure on the other levels
You have to find 3 Rusty Fragments, found randomly after invasions.
Certain invasions unlock certain abilitys. While invading an icon will pop up, to activate the ability click the icon
You have to reach Lv. 36 (you'll need to get a total of at least 97,000 exp).