I think I have identified these right but I am confused on the why part of my question. Am I on the right track or should I read some more?

Are these organic? If they are why?
KMnO4-no
CH3Oh-yes
C6H6-yes
PdCI2-no
Ch3CO2H-yes
Because they are carbon compounds, have covalent bonds that have low melting and boiling points. Inorganics do not contain carbon.

3 answers

I think you are close.
You will find that the distinction between organic and inorganic is often somewhat nebulous. Yes, in general, organic compounds contain carbon and inorganic do not...but not always!! for example, carbon dioxide, sodium cyanide, and sodium bicarbonate are generally considered inorganic. A better definition is that organic compounds generally contain carbon-hydrogen bonds.
Did I have the correct answers for the examples?
yes.