So what are quanta, and what kind of properties do they have?

This is not an easy question to answer. This is because the quantum world is far more extraordinary than we realize.

There is an "example" that illustrates this extraordinariness. This example is somewhat different from the properties of actual quanta, but by visualizing the following images would help you get mind around the properties of quanta.

Imagine that there is a pendulum swinging. A pendulum in the normal scale world swings repeatedly back and forth from right to left, doesn't it? But a pendulum in the quantum world moves in small spurts like the second hand of a clock going "tick, tick." just like watching a movie frame by frame. But unlike a second hand, it is impossible to ascertain what state the pendulum is in between one frame and another, no matter what we do. In the quantum world, there is no such thing as an intermediate state.

Consequently, it is not possible to represent the states of quanta as continuous units. In the quantum world, there is no continuous yardstick, nor is there a midway point on a scale.