Do you pray or say something every time before you eat? 

In Japan, we say "itadakimasu", which means " I'm being given." or "Thanks for the meal." It's difficult to translate this phrase exactly.

I think this phrase contains the feeling of awe towards other lives. (I don't know  if"awe" is the right word here; maybe "respect" would work better?)

Many Japanese people think of themselves as atheists, but now I notice now realize that this is a misunderstanding. Since ancient time, there are many gods and goddesses in Japan, and Japanese people have believed in all of them.

We have gods of fire, gods of sun, gods of tree, and also gods of toilet! I have heard the god of the toilet is a beautiful goddess. Don' t you think it's funny?

For this reason, we are tend to easily accept any other religions easily. We already have already tons of gods, so nobody cares (I would use "nobody minds" here) if some more gods come from abroad. That might makes us to feel consider ourselves atheist when we're and not monotheist.
We feel gods just next to us, not only in the heaven. And also we feel gods in plants, and animals and, even more, inside ourselves.

When we say "itadakimasu", we appreciate many things like people who grow plants and animals, who cooked the meals, and especially for other lives. (This doesn't make sense to me; do you mean to say "people who created other lives"?)

We need food to live, that means we need other lives called be it it plants or animals. So I think we should have appreciations to these other lives and their souls of them

This is great! You have a very sophisticated understanding of the English language. There are quite a few corrections here but I was being very particular. The ideas you convey in your writing, and the words you use to express them, are very impressive! Well done!

I personally don't say grace and I consider myself atheist but I think it's nice that Japanese people say いただきます before a meal, and I appreciated your opinion.