Do you believe in gods?

Depending on the religion, "god" is typically capitalized. (Christian churches) In this case could also be "gods" or "spirits"

There has been a faith which coois a belief in Japan called “Tsukumo Gami.” in Japan.

"faith" may not be best word. "Faith" sometimes implies a particular religion (in the US). US English: someone might be of the Christian Faith. But having faith also can mean believing in something. Faith with regards to religion vs believing in something that may not be directly tied to a church would be how I might describe the difference. It's a bit complicated to explain. 説明はちょっと難しいです、すみません。

It is the concept that everything surroundeding us could be the god if we use it carefullycome inhabited by a god if we take good care of it and use it for a long time.

Expressing this in English might be better like this: "It is the belief that the things we use regularly, such as household items, when used for a long time and taken good care of may become inhabited by a spirit. "

SoThus Japanese people has been cherishing things even it’sf they are old.

Rephrased so it's more natural.

Do you believe in god?

Alternative if you want to abide by title rules: Do You Believe in God?

There has beenis a faith which coocalled “Tsukumo Gami” in Japan.

It sounds like this particular fate still exists, so I rewrote in the present tense. However, if you write it to mean it no longer exists, you could say: There used to be a faith called...

It is the concept that everything surroundeding us could be the gGod if we use it carefully for a long time.

In the religious concept of a one universal god, it is referred to as just "God" without "a" or "the," and it is capitalized. However, for beliefs which involve multiple gods, it is different. It sounds to me that this is referring to a one universal god.

So Japanese people has been cherishing things even it’sf they are old.