ilah actually means diety (Im 99% sure).
The khalima is as fine as it is, There is no diety but Allah, and Muhammad is his messenger.
That's all you need to believe, because if you believe Muhammad SAW is his messenger, you have to follow his teachings which is that he is THE final messenger/prophet sent by Allah.
Just because ilah is translated as God doesn't mean it's always right, it's like the word 'Jannah', it actually means Garden or Paradise, NOT heaven.
Heaven means sky, if that makes sense, but Jannah is translated as Heaven because most people are used to using Jannah for Paradise or Gardens of bliss for example, and the word Heaven is used with hell normally, for example, Night and day, Male and female, Heaven and Hell.