pxCoveredCountopen keeps count of open child cases where as pxCoveredCount keeps count of all child cases irrespective of status.
pxAllCoveredResolved - There is no property with this name. I think you are referring to AllCoveredResolved. This is a Ticket set automatically when all covered child cases are resolved. In some specific situations, when it is appropriate to resolve all child cases irrespective of their status, we can set this ticket to resolve all child cases and conclude the case.