As for housing, I think that this would be standard econ, really. More money means more demand, which in the absence of more supply, means higher prices. Things like housing are harder to increase the supply of than say, TVs, so yeah, they'd probably go up more than the rest. But I suspect that everyone would still be better off.
I don't think rent-controls are a good idea. On the other hand, I do think that in the long run rich people gobbling up finite land is a problem;
What people want to purchase is not simply housing - it's housing in their preferred location.
I think a big part of what makes housing desirable, for the bulk of the population, is ability to earn enough of an income nearby. If that's the case, UBI might actually directly create desirable housing (out of almost desirable housing) and increase supply.
I don't expect this effect would be large enough that UBI would put downward pressure on housing prices overall, but I don't really know.
A UBI makes the pay matter a little less, and so makes places like that more attractive.
It doesn't, first order, cause more units to be built. But that is not the only way to increase supply.
Longer term, that kind of calculation about potential units, in places where it's easy to build, might lead to more units built. But that gets more complicated.