5 yr/unlimited miles is Toyota's corrosion warranty. Depends on what the rust is and how it's forming. If it's from rock chips, you probably won't get warranty help. But if it's from bad paint, you might. Get it in to the dealer and have it looked at.
The tailgate rust is fairly normal. My truck got its tailgate replaced by Toyota Denmark when it was 4 years old. The new tailgate started to rust also, but after it was sprayed with cavity wax the rust has stopped. I think the problem is well known, in europe at least.