Question about Shopify APIs by joep

Hi, I have read thru the API documentation and browsed the API forums extensively, but could not find an answer to my inquiry.

I am trying to determine if there are API call that can be initiated from Shopify when a user is using one of my potential customer's existing stores.

For example, can the APIs be used to do the following in real time? I am struggling to determine if the APIs can be used from Shopify to some outside service or if they are only used to call back to Shopify to perform data updates.

Here are a couple of questions:

1). When a user is in a store can an API call be configured to call out to a custom service to determine avability for a product?

2). Can a call be made out to a custom service to determine pricing and tax calculations

3). When an order is created can a call be made to a custom service to create the order in my customer's backend system.

Any guidance or pointers to other documentation would be appreciated.

Thanks.