No, this is something sure, Bitcoin will never fall back to 1000$. In fact even seeing it dropping to 2000$ seems very very unlikely to this point.

For such decentralised crypto-currencies, the price you see on exchange is how much people are ready to pay for it. Lots of people actually want to buy bitcoins at the same time, so they make the price increase, because they can pay higher than current price, and sellers profit from this by increasing the price at which they sell their bitcoins.

No, it could not, because since the beggining of the world, money creation is a ruler power, and it will always be.