My GF bought a kettle with copper finish. Looked really nice until water stains started to leave marks on it. It is now almost entirely covered with those darker gray-ish marks which I assume are some sort of oxidation. Is there a safe way to clean this?
Lemon juice or diluted vinegar (say 1:1), a rag and patience. Gentle and light scrubbing. Rinse afterwards and dry thoroughly.
The bad news is that it is not going to last very long. Even if you are not using at all, depending on your ambient humidity and temperature, it will tarnish again, albeit perhaps uniformly. It is still better to remove the oxide spots early. The longer you leave them, the deeper the oxidation goes. Every time you get rid of the oxide, you are actually removing a tiny layer of metal. So, if you have a copper plated kettle, at some point, you will expose the underlying metal. If it is solid copper, that does not matter too much.
Other than greyish black oxide, you can also have greenish carbonates too.
You can meticulously dry off all the water on the the copper surface especially before you heat it, and store it in a dry cool place, you can slow down the oxidation process.
Alternatively, let it tarnish and develop some character.
Is it an electric kettle or a manual one? A manual one on an open flame (electrical stove is fine) will make things harder for you because of water and carbon dioxide from the combustion products.