Here is an experimental particle physicist's answer:

If protons are made up of 3 quarks and those quarks are bonded with the exchange of gluons, why so many particles arise in a proton-proton collision?

It is mainly because of special relativity, the equivalence of mass and energy tied up in the E^2-p^2=m^2 rule of four dimensional space.

If the total energy is conserved, are those particles the transformation of the kinetic energy to matter?

Elementary particles are described by their mass and their quantum numbers. The same is true for composites of elementary particles, like the proton and neutron and all the resonances and the leptons. When the energy is available particles and resonances are created as long as the rest of the quantum numbers are conserved. For example there is conservation of baryon number, conservation of lepton number , in addition to angular momentum and momentum conservation.

So if the quantum numbers are conserved and the energy threshold for creating specific combinations of particles is reached , a probability exists that these particles will be created when scattering protons on protons at that energy, in addition with all the lower mass particles . This probability is calculated using the standard model mathematics using Feynman diagrams and quantum field theory .

The higher the projectile energy , thresholds for new particles can be reached and that is why higher and higher scattering energies are the goal in particle physics. Maybe new quantum numbers will be reached, i.e. theories beyond the standard model.

Here is an experimental particle physicist's answer:

If protons are made up of 3 quarks and those quarks are bonded with the exchange of gluons, why so many particles arise in a proton-proton collision?

It is mainly because of special relativity, the equivalence of mass and energy tied up in the $E^2-p^2=m^2$ rule of four dimensional space.

If the total energy is conserved, are those particles the transformation of the kinetic energy to matter?

Elementary particles are described by their mass and their quantum numbers. The same is true for composites of elementary particles, like the proton and neutron and all the resonances and the leptons. When the energy is available particles and resonances are created as long as the rest of the quantum numbers are conserved. For example there is conservation of baryon number, conservation of lepton number , in addition to angular momentum and momentum conservation.

So if the quantum numbers are conserved and the energy threshold for creating specific combinations of particles is reached , a probability exists that these particles will be created when scattering protons on protons at that energy, in addition with all the lower mass particles . This probability is calculated using the standard model mathematics using Feynman diagrams and quantum field theory .

The higher the projectile energy , thresholds for new particles can be reached and that is why higher and higher scattering energies are the goal in particle physics. Maybe new quantum numbers will be reached, i.e. theories beyond the standard model.