Does the IDF not have counter-battery radar?
Yes, of course; it is primarily useful against a repeating target (although we are working on that as well).
These are basically very large bottle rockets (with a warhead). There is no infrastructure but a rod or a plastic (poly-vinyal chorlride).
At the moment of firing, the criminal scoot away.
Typicall they shoot from behind roofs of houses or the like of people they don’t like, stores, etc., so it is difficult to return fire non-ballistically.