What correspondance for corresponding author?
All correspondence regarding the paper should go to the corresponding author (with very few exceptions).

If you should contact them with requests for clarification is a judgment call. If you are a student not understanding it, you should probably first discuss it with your supervisor. If you are an experienced scientist and believe that there is insufficient information or even an error, asking them would be appropriate. 

Me and my colleagues have also (successfully) contacted corresponding authors with requests for access to data for a meta analysis or to invite them to a workshop (all expenses paid).

So there are a number of legitimate reasons to contact a corresponding author. That's why the contact data is given in the manuscript.

However, from the perspective of a corresponding author, most correspondence you receive is usually with the journal (and spam from other journals and conferences).