I wrote "This is the peace symbol" and it was deemed wrong and it suggested: This the peace symbol. It is a symbol of peace.
The first suggestion is wrong and what I wrote is the best translation if this is meant to name this symbol: ☮
The second suggestion is a poor one if the idea is "☮"
Is there a grammatical way to tell if someone means "room" or "peace" or is it mainly through context clues?
No, the declension is identical. (Sometimes it is different for different meanings, true.)