There's no "reliable" way to do this, as you're interacting with one or more shippers. After shipping physical product around the world since... 2003... every shipper only gives ballpark windows of when they can complete a delivery. Using Amazon FBA will likely provide fastest delivery times.
If its for sales through Amazon (or even elsewhere) FBAPrep.com is one of the best out there. They can handle importing, preparation (repackaging, barcoding, etc.) and then final shipment. Plus, they know the special requirements of Amazon and other third party marketplaces.
You're already saving by using a fulfillment house in each region. You could save a little more on costs by sending the product to the 3PL already picked and packed. If your product is repacked in a mail-ready package that will save some. You could take that one further and send the picked, packe...
These are all specific questions you need to be taking to a Tax attorney, or accountant. The laws are varied on all of your issues and need to come from one of the places I just suggestied, and not from a get help site. Good luck