Short answer is yes! If this integration is just for your own company's Shopify shop then you can create a private app (https://help.shopify.com/en/manual/apps/private-apps). Otherwise if you are a service provider you would build a public app in a development store for resale. Either way, from there you app can use one of a variety of different API types. Here are a couple:
Hope this helps!
Definitely. First step would be having a technical resource at your disposal start reading up on the private app link I provided. From there they could create an app either using the GraphQL API or the REST API that would pull order details. Those API references are in those two other links I provided. Good luck!