Everyone getting it buys a lot of the same goods, including housing. You'd expect increased demand to bring prices up a bit across the board, but I don't think it's as huge as you're making it out to be.
It will rise inflation, probably - as you will have a lot more cash in the market... And finally "nothing will change".
Inflation isn't really tied directly to cash in the market and I doubt you'd see inflation soak up $1000 / month. The dollar would have to become basically worthless for that to happen.