How does chlorine form more than 1 bond?
The order of bonding, and so the valence state of Cl in $\ce{ClO_{x}-}, x&gt;1$ compounds is very debatable. Generally, two models exist. 


$\ce{Cl}$ atom, just like $\ce{S, P}$ and some others has unoccupied $d$-orbitals in the valence shell. It is possible to move some electrons from $p$-orbitals to $d$-orbitals, producing half-occupied orbitals that can participate in covalent bond formation
$\ce{O}$ atom has 6 electrons at the valence shell with four orbitals. It is possible to move one electron from chlorine atom to oxygen atom to form $\ce{O^{\dot{-} }}$ ion, that can than form a bond with newly formed half-filled orbital of chlorine. However, being electronegative and having high positive charge, chlorine partially pulls back the electron pair of newly formed bond.


Currently the second option is in favor of theoreticians, both by electron population analysis and relatively high charges in the oxochloric compounds, however, in school-level chemistry people traditionally resort to the first option. On the other hand, the second approach is the only option to adequately describe nitric acid and nitrates as nitrogen does not have $d$-orbitals on the valence shell.

Now, the stability of oxochloric compounds is a completely different matter. All of them are not very stable compounds, easily freeing their oxygen. Still, the process has significant activation energy, the state in between is even less favorable then oxochloric molecule. both oxygen and chlorine have electron-rich shells that repel potential reactants. Perchlorate ion is especially stable, at its surface is completely covered by outer negative shells of oxygen, so electrons cannot reach positively charged chlorine.