So my question is that, does the photoelectric effect work for only valence electrons?
Impacting photon energy goes like this :$$ h\nu = E_{_{ionization}} + \frac {mv^2}{2} $$Ionization energy depends on exact energy level where electrons occur, in what shells, etc. So the answer is that in general photoelectric effect applies to all electrons, simply there's biggest chances that photon will knock-out electrons from outer shells, because these have lowest ionization energies, thus has lower thresholds for photon frequency.
why doesn't the element selected turn into plasma?
If light has required high frequency for passing ionization threshold and comes in high intensity, then yes - material is converted into plasma. That's how Laser cutting works.
