A problem here is that "drone" could mean anything from a mostly plastic, under $500 RC quad copter to a military drone that's got the 130 foot wingspan of a Boeing 757. The detection challenges are rather different.
Something small enough to drop a small explosive (like a hand grenade) on a group of troops is a real concern and can be small.
For your hard questions, "Have you ever had to develop or use an advanced, proprietary antenna for a project to proceed? How did you develop the antenna configuration and then analyze its likely performance?" For obvious reasons, one can't talk in too much detail about this, but the modeling was based on commercial antenna software (Agilent HFSS, or even NEC derivatives) but also had some pure math involved handled in Matlab or Mathcad. Simulation problems scale with the number of antenna elements and can cause them to run for a long time before they barf and stop working. Symmetries, like the rotational symmetry the IsoLOG displays can simplify the math and keep the simulations from diverging. For these reasons, the systems are generally ones that the most senior designers can envision.
Simulations only get you so far, then a lot of field testing is done.
There really is no substitute for engineering experience. Yet.