Of your examples, only #4 would not typically be heard in North America. #1 and #3 are most common.
Very generally, if something is broken, it is seperated into more than one piece. By broken down, some machine or mechanism is no longer functioning, but it is still in one piece. There is no hard rule for how we (NA) use these terms, and there can be some overlap.
We wouldn't say our watch is 'broken down', we would say, "My watch has stopped." OR "My watch is broken."
I don't know if this will help or only confuse you more: It would be quite common to hear someone say, "My car broke down on the way to work. Something must have broken."