Water pressure low and lack of hot water - Do we have a faulty boiler?

It sounds like you have a hot water leak. Somewhere in the hot water piping there could be a leak. This would explain low water pressure and lack of hot water. To test this; put a pressure gauge somewhere on a hot water line and turn the cold water feed to the hot water heater off. If the pressure drops , you have a leak. Usually these leaks happen under the floor and are hard to find and fix. For sure you should call the landlord and make him deal with it. A competent plumber could easily diagnose this.................