Depends on the scale of your operation -- we have employees for each function.

For a modest operation you could cross train 1 or 2 employees to handle the tasks you mention in house.

If you process direct you can handle a lot of customer support functions internally and resolve many payment disputes as your merchant account will (or should) give you chargeback codes and some customer contact information.

When you turn a customer dispute into a satisfactorily resolved issue you gain the respect of your customers, their loyalty and positive word of mouth referrals -- those are gold in any business.