I think in the main you've the right idea. But for CO2 you're focussing on the whole molecule, rather than the bonds. If the oxygens pull (what) on the carbon, what implication does that have for the bond?
The situation is the same for SO2 but fortuitously the existence of the lone pair has led you to the correct conclusion.
Depending on the level you're asking the question at, you could argue that there is not complete electron transfer from Li to F, so very polar covalent, but this is more a mathematical and philosophical question.
S