Bitcoin works regardless of the price. There is nothing to worry about, even if it drops below $1.
This is incorrect. The concept "works" but for practical purposes Bitcoin does not.
A) Bitcoin, with its existing 1MB limit on blocks, is limited to 7tx/sec (according to Bitcoin Wiki). Bitcoin's market cap and average BTC per address directly affect how much wealth can be transacted through Bitcoin in any given period of time. Therefore it directly affects how well the Bitcoin system can function as a payment processor.
Fortunately we aren't anywhere near the limit, and we can adjust the limit in the future if we encounter it and there is enough agreement from the community.