Please refer to below document for obtaining the whole category tree and do the mapping between categories from sellers and categories from Aliexpress.
https://developers.aliexpress.com/en/doc.htm?docId=117929&docType=1
Please refer to below documents
https://developers.aliexpress.com/en/doc.htm?docId=116676&docType=1
Use Query order list to get lists of orders. The results can be filtered based on order status.
Basically, Aliexpress supports two types of order fulfillment/shipping: fulfilling orders by sellers or fulfilling orders by Aliexpress. Currently fulfilling orders by sellers is a more common scenario for oversea sellers. Please pay attention to the following document.