Will will ! a resident throws a bag full of trash over the balcony of their third-floor apartment. what will happen to the acceleration of the trash bag as it passes the second and first floors?

The acceleration will be the same all the way down.  If this resident is still being allowed to live on Earth, then the acceleration will be 9.8 m/s² downward.

It doesn't matter how much trash is in the bag, how heavy it is, how big it is, how small it is, how much mass it has, or what color it is, and it doesn't matter whether the inconsiderate resident throws it up, down, or straight out horizontal.  The acceleration is 9.8 m/s² all the way down, until it hits the ground, splits wide open, and strews trash all over the neighborhood.  Because 9.8 m/s² is the acceleration of gravity everywhere on Earth.