How does one develop artificial stabilization for aircraft uncontrollable without it?
Most modern high agility ariplanes (such as fighter jets) are unstable in the sense that (among other things) their center of gravity (nearly) coinsides with their center of lift (i.e. they are wildly out of balance). The benefits include the ability of the airplane to react to control inputs nearly instantaneously. That the design will be unstable can be determined at a very early stage in the process (during the 'sketch' phase, really). Given a fast enough control system, nearly anything can be controlled (and modeled) so to answer your second question, to design a control system, all one needs to know is how complicated the system is (the order of the system) and how fast it should be. The first question can be answered based on very general principles (most aircraft can be modeled by a fourth order system). The second question is also easy to estimate (100 Hz is usually enough, don't ask me how I know this).

Of course, tricky regimes (supersonic, transonic, supercritical angle of attack, etc.) might require some time in the tunnel but these are to determine some parameters of the general model that has been decided on at the design stage.

That the system works is usually not in question before the plane is tested. Whether a human pilot will find it controllable is another matter. This is why the design of a modern high agility aircraft is done in parallel with a simulator design to see how the pilot would react. The simulator of course, is based on the same model that the actual design is (and is constantly modified as more experimental data becomes known).

Finally, even if the airplane is well designed, and everything works, the certification stage is where most accidents happen. For example, to test the single engine performance of a twin engine airplane the tests must be carried out at near sea level pressure, quite low to the ground. Not much time to react when the plane gets too slow.

A good book to read about these issues is Aircraft design: a conceptual approach by D. Raymer. You will quickly discover that one can practically calculate the look of the plane (controls location, high-wing, low-wing, where the engines go, etc.) based on its mission.