You can elect to participate in Amazon’s “Inventory Placement Service,” where Amazon will assign units of a single product/ASIN to a single fulfillment center. You are only responsible for sending your shipment to that one assigned fulfillment center; after the shipment arrives, Amazon will split it up and send it to different fulfillment centers for you.
No. Amazon will determine which fulfillment center a shipment of a product is assigned to.
No. If you have multiple products/ASINs in one shipment, the shipment may still be sent to multiple fulfillment centers. If you have different unit types of a single product (ex. standard size vs oversize), they may be directed to different fulfillment centers.
See Amazon’s Help Center for program fees and more information.