Is it similar to the gold key on level 6? Can it be used to grab more of the treasures there, or does it only fit the door at the end of level 3?

Those keys are used only for those 'treasure' doors/gates.


SPOILER

There will be more than one on those doors/gates with treasures :)

So they are indeed similar?

the diffrent keys have set looks on their locks, so logically you could save that key for the later levels to open an extra door of those, however i havent tried that yet so no comfirm. but yes same type of key same type of lock so it might be possible.
thou in general most of the extra rewards in the spare rooms usually dont atract mutch attention to bring an extra key, atleast it didnt for me when it came down to choice. but everyone is different ofc ;)

To tell you the truth I don't remember how those keys look like. But if you have a golden key that doesn't fit anywhere but in the treasure doors' lock then if you will find more of them you may be sure it will fit there. Some suggest to keep those keys and use in another treasure room.