Hi there I am a total novice, and would like some help please my problem is

we have just moved into a house and have a backboiler ( the fire doesn't work the landlord says it is due to a flue problem, I don't think this can be right cos if it was then the central heating and hot water would not work either) am I right in my thinking please?

second, we have an overflow pipe that is dripping, The landlord put this down to the power shower, put we have noticed that if we turn the hot tap on the dripping stops for a while. also when the central heating is switched to off and the hot water is on, the three rads & towel rail upstairs come on, and if we turn them off the three rads down stairs come on.

Any ideas what can be causing this problem.