For example, is mining required to produce computations to support the system, and if so, how would the system manage a massive decline in mining with a surge in transactions?
Miners don't "share the load" but rather compete to find an answer to the same problem: a nonce for the next block which makes the block header hash smaller than a certain value. The difficulty of this problem is set artificially (but by distributed consensus) to keep the rate of new blocks being created at about 1 per 10 minutes.
If a lot of miners quit, the difficulty is automatically lowered and transactions will continue to be confirmed at the same rate. In this sense, it is not necessary to have a lot of miners.
However, this does make the network less secure because it makes it easier for an attacker with a lot of computing power (i.e. more than 50%) to make large changes to the block chain. That would enable double spending attacks among other things.
To prevent miners from quitting, transaction fees would have to compensate for the reduced block reward. So the real question is: what will the transaction fees become as the block reward tends to zero? And will they be enough to keep the block chain safe?