So you know that Copper is a 2+, so just apply the rules of the type I, except this time put the charge after the cation, leaving you with Copper (II) Chloride.
Type III:
Non-metal and non-metal. These one are easy! after you made sure that the elements are both non-metals, just use prefixes to name them. For example, if you had H2O, you would call it dihydrogen monoxide. Remember that if the cation, or the first element, has just one atom in the formula, do not use the mono prefix. Here's a list of prefixes:
1-mono
2-di
3-tri
4-tetra
5-penta
6-hexa
7-septa
8-octo
9-nona
Heres some more examples: SF6= Sulfur Hexafluoride (note it is NOT monosulfur hexafluoride)
CH4- carbon tetrahydride
Hope this helped!