As for her "partner" and how he can be a partner while living in another house is a mystery, just google the availability of one-bedroomed council stock and see what you get. There isn't any, hence the insanity of the bedroom "tax".
That depends entirely on where you live echt. In the City of Manchester, where I am, there's a huge shortage of one bed SH properties except those which are specifically for over 55s. For those, supply and demand are broadly matched. Basically, if you want one, you'll get one soon enough. There's also a shortage of two bedroomed properties full stop, and these are in great demand now from families because of the bedroom tax. Meanwhile, pensioners exempt from the bedroom tax are able to under-occupy two, three and four bedroomed properties while families rot on the waiting list. Single pensioners or couples can even be given two bedroomed properties as new lets, because as there's a shortage of one beds (even though there isn't if you're a pensioner) HAs allow people to bid for properties with one extra room. There's something very, very wrong with that picture.
I'm not a huge fan of the bedroom tax, or not as a national policy at least. I can see that it perhaps needed doing in London and the south east, but there are plenty of areas of the country where it wasn't needed at all. But if it's staying, it needs to apply to pensioners too.