Do Palladium(II) Chloride and Palladium (III) Chloride follow 18-Electron rule or octet rule? How to determine this?
Palladium (II) Chloride follows neither the 18 electron rule nor the octet rule.  

Instead, like many Pd(II), Pt(II) and Ni(II) complexes, palldium (II) chloride follows the 16-electron rule.

Pd(II) generally forms square planar complexes, and in palldium (II) chloride each Cl bridges two Pd, with 4 Cl coordinating each Pd in a roughly square planar arrangement.  8 d-electrons plus 2 electrons from each of 4 sigma bonds equals 16 electrons.

I have never heard of "Cl3Pd", which would involve the rare oxidation state Pd(III), but the 16 and 18 electron rules should only be applied to diamagnetic complexes.  Pd(III) complexes are paramagnetic.