The problem with fulfillment directly from China is they don't have the same rates as you would get once you've brought the product to your country for shipping. Then the issue is with customs and it is much cheaper to ship over in bulk, then hire carriers to ship to each consumer, assuming you are talking about B2C customers. If you are talking about B2B, if the quantities are large enough, then perhaps this might make sense.
The better path is to ship them to your fulfillment warehouse and send out the orders directly, plus higher margin and greater control. There is some great software out there to help you accomplish this (skusavvy.com - created for this).
Yes of course. More and more dropshippers start to dropship from 1688 Taobao which need agent offers sourcing, purchasing, QC, repacking, warehousing, pick pack and shipping as well as custom label pacakging service to fulfill from China to clients.