Each bitcoin can be divided into 100 million atomic units called "satoshis". 1 BTC is just a particular denomination, in the same way that $20 and $100 bills are denominations in use for USD.

1 BTC is a historically common denomination that will likely receive less usage if the price continues to rise.

Sure, but thankfully you don't need a whole coin for most transactions. It's not an inherently meaningful thing.

But it is a psychologically important thing, and Bitcoin price has always been psychologically driven.