As I understand it, you are saying that the lease states that it will provide the heat, hot water and gas to the apartment. But you are unhappy because you found out after moving in that there is no heat to the bathroom? Is that what you are saying?

I think a judge would say that 'you saw the apartment before you moved in and you saw that there was no radiator or vent that provided heat to the bathroom. Therefore, the landlord is not obligated to make any changes to provide you heat to the bathroom.' Good luck to you. Those little radiant heaters that sit on the floor and plug into the wall work nicely in bathrooms. If I were you I'd get one.

The landlord installed an electric heater in the ceiling in the bathroom and connected the thermostat to the circuit breaker box. I therefore would be responsible for the cost to heat the bath room.

Yes, your lease is a legally binding contract.

Why would you not want a source of heat in the bathroom???

If it is for a year or more. Yes, terms of leases do not specify which rooms are heated, just who pays.

Yes.

yes it is