So the Goose in my backyard, should I give it water?

If it has no other access to water, then yes. Give it enough water that it can submerge its entire bill into it becaue geese need to occassionally flush out their nostrils in water. Eating grass is completely normal for geese & is actually good for them because they need the niacin from it. They're very good grazers, almost as good as sheep or cows.