How to Build Military Drones?

I don't know who designs and assembles the complete drone, but I do know that almost all of the components in the military equipment of western countries are outsourced to traditional private aerospace companies, such as Honeywell and Lockheed-Martin in the USA and Thales in France.

My personal suggestion for doing anything related to aviation and software is to get very familiar with linear algebra. There is practically nothing in kinematics, navigation or robotics that doesn't have matrix operations at its core. To bridge the gap between this rather theoretical field and CRUD development, you might want to look into declarative programming and 3D computer graphics, both of which lean more towards abstract linear algebra.

Could you get some cheap drone and rig it up so it can carry something small and the drop it? Then write some software to go somewhere on GPS and drop something there autonomously?

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DJI Mavic series drones are popular for military applications