I'd kindly appreciate any insight on the below questions, I couldn't find an answer in CSW or here.
1. Does each Shock need to be fully resolved before we move to resolving the next one, or do we need to resolve the first phase of Shock (Charge) for each Shock attack and then move on to the second phase?
Each step of shock is resolved for all shock instances before moving on to the next step.
2. Can a Skirmisher move, fire the sling, move, then fire the sling again? Can they fire at the same unit twice?
A unit may fire once at any time during movement. This can be before, during, or after moving.
3. Can a Skirmisher shock attack? The rules say NO, but I've seen an article where skirmishers are used to finish off routed units.
I don't think they can, but I do not have the article you mention.
4. Which happens first, entry reaction fire of the static unit or fire of the moving unit? What if one of these 2 fires routs the other unit, does that unit fire at all?
They are treated as simultaneous if memory serves.
I hope I was able to help!