Just to note, the term drop shipper references the wholesale supplier and not you, the retailer/reseller.
Drop shippers differ in how they handle shipping. There are some who include cost for this in the drop ship fee, some will be charging a flat fee, some will base this fee on the weight or on the price. It would be best to carefully read the supplier's policies and procedures and if things are not clear, you just need to ask. Custom /import duty fees, on the other hand, are always shouldered by the buyer.