Does the surface area of an object affect how fast it falls?

Yes

Explanation:

If an object is flat and it falls it will go against the air (Air-Resistance) when falling down, which it will make the block go slower then a sphere which has no sides and will fall faster then the square or Block because there isn't a flat side it wont go against the air ( Air-Resistance).

the density(ratio between mass and volume as m/v) decreases from top to bottom in periodic table group as the size increases and nuclear charge decreases. but in periods density increases from left to right as atom size decreases and nuclear charge increases.