Do the Vimar control units with keys all have the same key?

No. Each pair of keys provided has an engraved number that indicates its correspondence with the code engraved on the lock. If you need to make duplicates, you must request neutral keys from Vimar and make a copy at any hardware store. Vimar also provides controls with keys coded "000" in order to operate multiple controls with the same key: these items are shown in the catalogue with the suffix ".CU".