2) The American housing market is very messed up and far from a free market, so any prediction up or down is very difficult. I predict that Basic Income will cause a bunch of people to move from high cost cities like NYC & SF into low cost areas so that they can live comfortably on the basic income. So there will be pressures both up and down on prices. But point #1 still stands. Right now most Americans already have a place to live, and basic income isn't going to cause people to go out and buy a second house so the effects are only going to be at the margin.
3) According to most economists, inflation is always a monetary phenomenon. If you print money to pay for UBI, inflation will go up. If you take from the rich to give to the poor, inflation will stay constant.