The Planck units are a choice of natural units relevant to cosmology. They aren’t the smallest or largest of anything. The Planck mass is roughly the same as that of a fruit fly.
In our current established theoretical framework, there is no reason to presume that either time or space are discrete, nor is there experimental evidence for it.
The Planck constant [Js] was introduced to find a way around the UV catastrophe. The Planck length [m] is defined as \sqrt{\frac{\hbar G}{c^3}}, where G is the gravitational constant and c the speed of light in vacuum.