Will a bullet land at the same rate as a ball If you drop or shoot it at the same time and the same height?

Yes. The rate at which something drops is not related to its weight. However, one should not neglect air resistance, which can play a big part. For example a person on a parachute falls much more slowly than someone without one, simply because of air resistance. Similarly.a feather woudl fall more slowly than a garin of sand of the same weight.

But, if you had no air resistance then all things would fall at the same rate, even a bullet moving roughly parallel to the Earth's surface as a high speed.