How to make sense of audio file's $\textrm{dBFS}$?
However, the dbFS values I'm getting are consistently below -20, i.e., 10% loudness, even at loud parts of the song. Why is this so? Am I calculating the loudness wrongly?


Why should that be a problem? Human perception is roughly logarithmic. Sound that isn't "unbearably loud" shouldn't be much more than 10% of your "acoustic dynamic range".

By the way, with $\frac{}{20}$, this formula gives you amplitude, not power values, so this isn't truly loudness, just amplitude. But since that, in perception, is but a constant factor, these terms can be used interchangably.


  Also, how can I calculate the overall loudness at a point in time? Is it the sum of all the values, or the maximum?


It's the sum, at least approximately: human perception has a different sensitivity for different frequencies, and also, frequencies can mask each other, so the energy in the signal is only proportional to the perceived loudness if we ignore these facts (see: psychoacoustic models).