Carbon has four valence electrons. Meaning, it has 4 electrons in it's last shell. These 4 electrons will form a covalent bond with other elements to get the full set of 8 electrons needed for it to be stable. That is why it's considered as tetravalent.
Here is the graph, hopefully the next person can get it
When a liquid is frozen, the atoms in the liquid slow their movement due to lack of energy so the substance becomes hard.