X The automated external defibrillator is set up in congressional in the this hospital.
There are three problems with the English on this sign.
If you say “The automated…”, we would assume it’s the only AED, or it’s a specific AED that has been mentioned before. But it hasn’t been mentioned before, so “an” is better.
Someone has translated 「設置」 as “set up in congressional” — it’s hard to be sure what that means! Americans might think it has something to do with their Congress (国会)! A better translation is “installed”.
Also, as you probably realized, there’s no reason to have “the” and “this” together. You only need one or the other. In this case, “this hospital” would be better, because it means 「当病院」; “the hospital” is simply 「その病院」.
O An automated external defibrillator is installed in this hospital.
X This water is normal temperature. The person needing ice, please use an ice machine.
What temperature is “normal”? Are there temperatures that aren’t normal? What this sign means to say is that the water is room temperature.
“The person needing ice?” Only one person needs ice? I assume that many people will want ice! In America, the sign would probably address the reader directly with “you.”
Also, if you say “please use an ice machine”, it tells us that you don’t know where any ice machines are located. (Or, it could mean that there is more than one ice machine available.) But from reading the Japanese on this sign, we can see that there is an ice machine in the same room. Therefore, this sign should use “the” before “ice machine.”
O This water is room temperature. If you need ice, please use the ice machine.
Pets do not go IN the grass, they go ON the grass. Much smaller creatures, like snakes or insects, would be found IN the grass.
The structure of the sentence is also a bit strange, and “Pets” shouldn’t be capitalized in the middle of a sentence. Of course “Pets are not allowed” would be more correct, but on a sign that gives instructions, we often skip simple words such as “is”, “are”, and “the”.
X …except for the designated some restaurants where…
This is partly a word-order problem, but also, they didn’t need to use both “the” and “some.” “Some designated restaurants”, “the designated restaurants”, or even just “designated restaurants” would be fine.