The protocol self adjusts so that it's always profitable to mine bitcoins

As it becomes unprofitable miners stop, and the difficulty drops so that it becomes cheaper to mine, until it reaches an equilibrium

The adjustment algorithm still requires blocks to be generated before it adjusts. If enough miners shut down at the same time, time between blocks will skyrocket, pushing the difficulty adjustment forward even further and crippling the transaction throughput.

Is the difficulty dropping because miners are then racing against less miners, or is it a different mechanism?

Different mechanism, Bitcoin's difficulty adjusts based on how quickly blocks are mined so that on average 1 block is mined every 10 minutes.

The protocol adjusts every 2016 blocks, if it takes longer than two weeks (20160 minutes) to mine the 2016 blocks then the difficulty decreases, if it takes less than two weeks to mine 2016 blocks then the difficulty increases.

It really depends from miners to miners. As effectively it's about how cheap your energy cost is. Since there's no transport cost, your cost is to acquire cheaper energy.