Important addition: Most statements regarding Planck units are hypotheses or educated guesses at best. (Other people call them numerology – because people simply combined some fundamental constants and out came the Planck units.) We don't really know whether there is a minimum length or minimum time, what happens at the Planck scales etc.

These are the scales at which neither General relativity nor the standard model (QM, QFT, etc) dominate, so you cannot just ignore one and do the calculations with the other. To solve systems at these scales, you need a working system of quantum gravity. We do not yet have one of those. These quantities are essentially where our current models of physics break down and we can no longer make anything resembling a prediction.

Not a physicist either but currently self learning quantum physics. Note that Planck length and time are just units - they do not mean that space and time are quantized. Quantum theory treats space and time as continuous variables. While it has been speculated that space and time are quantized I do not believe this has been experimentally verified because the scales involved are beyond current experimental reach.

> the Planck length is presumed to be the smallest measurable distance before stuff turns into a black hole

This is not correct. The Planck length happens to be very very roughly the scale at which we expect effective theories that ignore quantum-gravitational effects (i.e. the Standard Model) to break down. It has no special physical significance.