Xenia's poverty was relative. She was obviously living a good deal more modestly than she had before the Revolution, but quite comfortably by most people's standards. Yes, she was got at by fraudsters, but also she seems to have been somewhat naive about money (unlike her sister Olga). It would be going a bit far to describe her as profligate, but she didn't have much financial sense, and to judge by what John van der Kiste has to say, she was quite content for her sons to be a bunch of drones and live on her largesse.
'No heating' presumably means no central heating and managing with a open fires (basically a fire in the drawing room - with a 'back boiler' for hot water - and fires in the bedrooms only when someone was ill). For houses not to have central heating was far from unusual in Britain at the time Xenia lived here. From my own experience (I was born in 1959) central heating didn't become the norm until 1970 and after - and my grandparents' house in a middle class area of Liverpool didn't have electricity until the 1950s (the household managed with gas lighting).