The box in question is a 55cm cube. Do we also need to buy a ticket for it or something?
No, you don't need to buy a separate ticket. It is very common to see tourists carry a large baggage in public transport, especially the train from and to the airport.
There are always some people who are annoyed with it, but they are not the majority. If you care about those 10% people you can do nothing.
The more hassle is that it is common that you are unable to find any elevator in the metro station, and also there is no escalator. So you must carry your baggage on the stairs.