Discussing APIs and development related to customers, discounts, and order management.
We are looking for a way to use Shopify to help our customer service group fulfill warranted parts and finish good replacements. Can we send no-charge warranty replacement parts orders initiated by our customer service group from our Shopify site (FYI ... parts are listed and sold from our website)? Similarly, can we send a no-charge warranty replacement for the finished goods? Is there any 3rd Party apps for Shopify that can assist with this?
If "no-charge warranty replacement parts" are either free products or discounted 100% then yes you can create those orders same as a normal order. You would just discount 100% and give the reason.
For "Similarly, can we send a no-charge warranty replacement for the finished goods?" If you're asking can we send a free product, yes.
"Is there any 3rd Party apps for Shopify that can assist with this?"
You don't need an app to do this.
If that doesn't answer your question, it might be helpful to reframe the question of what exactly you'd like to do in Shopify, someone should be able to tell you how you can achieve it.