Shopify and Amazon Integration

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I am doing some preliminary research on opening a store that will contain some items that will be sold only via Shopify and some items that will be solid via Shopify and Amazon. I would like for the items sold only via Shopify to be fulfilled by a private fulfillment service that uses Shopify's platform to fulfill items, while the items that will be solid on both Shopify and Amazon to be fullfilled by Amazon.

Additionally, I would like to manage the inventory of the items sold on Amazon and Shopify via the Shopify inventory management platform. 

Is this possible with the current Shopify and Amazon integration?

Lastly, for the items sold on both Shopify and Amazon, will customers that buy these products via the Shopify platform still get the same Amazon shipping benefits (i.e. free 2-Day for Prime members)?