Amazon will not provide service for what they sell. If you have a unit bad out of the box, they will replace it or refund the money. If Amazon is selling for another party, they will refund your money and send the unit back to the actual seller. Customs duties remain the same, but will be correct, not like the current system of a single international shipment where the duty is calculated by an individual who might be right, but due to the complexity of the law is probably wrong.
AV equipment will not cost as much for shipping because most of it is made in Asia. Books can be printed and bound in India, giving a few Rupees to the local economy.
Amazon makes it very hard to get them on the telephone. I doubt they will have much of a call center. The majority of their phone work is customer care to sort shipping problems, and problems with the goods. To place an order, or make inquiry you can leave the phone on the hook. It is all done online, by self-service.
Fulfillment in India is to save Amazon money. They already do business in the country, but the paperwork burden is costly for international shipments. They ship from UK because the British invented red tape, and are well suited to deal with it.
With a center in Mumbai, domestic shipping will be very reasonable for them. One of Amazon's dirty tricks is to delay your order unless you commit to additional charge to get the item moved faster. They offer "free" shipping with a nominal purchase, but will sit on the order for five days to see if you place another order, then wait five more days. The "free" shipping is actually included in the price of the goods. If you will pay more, they print the shipping order faster in the godown. The package will still move at the speed of the dabbawalas carrying it.
