1) Who determines the value of the new forks when it started {BCH at 2017/8/1 }.
2) if new forks starting from 0 how can claim my BCH {get my free BCH }.
3) after new forks starting it will have huge demand and a few supply why it keeps increasing.
Let's consider your question:
1) No one puts the price, this is a way out of demand and interest on this coin
2) If during the fork you had bitcoin, then it will appear automatically. And if you did not have bitcoin you were already late
3) Because of capitalization and because there is little supply, in the market there is a demand for a coin, but sometimes it happens that this is just a game of whales