Nitrate is fine, in fact it's normal/good to have some in a planted tank. Ammonia is a problem, the bacteria should convert the ammonia produced by the fish into nitrite and then on to nitrate which you'll plants will then consume. Ammonia and nitrite should be zero, nitrate should be low but not zero.
Your filter needs to be running for the bacteria to stay alive, they'll start to die within hours from the lack of oxygen, and then when you turn it back on the dead bacteria will spike ammonia. Your best option is to keep the filter in with the fish, so move it to whatever tank they are in.