If they deem your situation covered by warranty, they will likely sent you a new drone, that's what they did for me. If they deem it pilot error, they will quote you a price to fix it and charge you for the labor and materials. Usually if it's covered by warranty, it's determined prior to shipment by evidence you provide them, such as the flight log and video of the flight. If they deem it covered by warranty, they usually send you a prepaid shipping label.
I've heard the sensors will not always detect small thin objects like wires or small tree limbs without leaves. So avoiding trees may not be me covered under warranty, unless you can provide some evidence showing what happened, enough that DJI can deem it compelling to justify warranty coverage. You'd have to prove the craft has OA enabled, etc.
When you say you hit a tree, that sounds like pilot error.
As for your accessories, don't worry about that. DJI usually asks you to NOT RETURN any accessories, including no props, no SD card and no battery (assuming your battery is OK). If the battery was damaged, then yes, you should return the battery. You usually don't need to return the controller either, they don't want it if nothing has happened to the RC.
I'm surprised you didn't get these instructions from DJI Carson when you requested a warranty repair. Are you in the US?