Prestashop automatically product import and scheduled order export script using API

General information for the business: We build webshops and websites
Description of requirements/functionality: The idea is to make a connection from a Prestashop multistore environment with my back-end system, which handles the orders and has all the information about the products.

I want to be able to automatically import new or updated products into Prestashop including the product image, quantity, description, price etc. and I want to be able to export the payed new order or updated orders from the Prestashop.

I'd like to make use of the Prestashop's API and make use of XML format.
Specific technologies required: PHP XML Prestashop API
OS requirements: Linux
Extra notes: