Quantum mechanical particles are very different things to classical ones.

A slightly better way of thinking about them is quantised fields. Particles and waves are simplifications of the underlying effect. There is no classical equivalent to work with to this, so we try and understand it as particle-wave duality etc.

In this case, a carrier particle is a (quantised) disturbance in the underlying field. If it has enough energy, it manifests as a physical particle. The higgs boson is an example of this. Below the required energy, you get virtual particles. These "borrow" energy, and so can never be seen directly, only inferred.

By example. Photons are the carrier particle of electromagnetism. Give the field energy and you get photons (light). Without that energy, the photons are virtual. Existing only between the 2 acting entities.

Different fields have different carrier particles. The photon is quite simple. It's effectiveness decays as 1/r^2 . The strong force carriers are more complex. They can emit more carrier particles, allowing the field to grow with distance rather than decay.

To add more complexity. The various fields look to be aspects of the same field. At sufficient energies, they behave identically. We have figured out how to combine the electric, magnetic and weak fields. We have a handle on the strong field. The higgs field seems to also match into this. Gravity is a pain to study. We assume it should match in, but haven't managed to work out how yet.

As for why the underlying field exists and follows the rules it does? We have no clue right now. The 'why' tends to follow the 'what', and we have yet to get a good handle on the 'what'.

diamagnetism, paramagnetism and ferromagnetism can be fully explained only using quantum theory

The magnetic properties of certain materials (e.g. why an unmagnetized piece of iron sticks to a magnet of either polarization), the way permanent magnets work, is best explained by quantum mechanics.

However, the electromagnetic force itself doesn’t “arise” from quantum mechanics, and you can explain things like electromagnets and a lot of common electric circuits (until you need a transistor) quite well without considering quantum mechanics.

Usually you take the “classical” formula for a force and to inform your quantum mechanical model of particles, and that’s how you can arrive at things like deriving how permanent magnets work with the help of w quantum mechanics.

Generally, a lot of material science and chemistry is inherently quantum mechanical because the way atomic orbitals and molecular bonds work is heavily quantum mechanical.