Yep. As it becomes more profitable more people mine, the difficulty goes up, profitability goes down, people stop mining, difficulty goes down, and so on.

That's correct -- the difficulty to mine BCH will reset at block 479,808 (the last adjustment) + 2016 blocks (the number of blocks in between each difficulty adjustment).

The difficulty of mining BCH is currently expected to increase at the next difficulty adjustment, and thus profitability will go down.