What difference would there be in the density of shotcrete before and after shooting? Is there any shotcrete mixture-design software in SI units available? Or any document of shotcrete mixture design in SI units for optimizing shotcrete design?

Shotcrete is simply a placing method for concrete. Thus, the mixture design and material properties are the same as concrete. We are not aware of any software specific to shotcrete in any units. ACI 506R-05, “Guide to Shotcrete”, has guidance on desirable mixture characteristics (aggregate grading, supplemental cementitious material [SCM], and so on) that would be helpful in developing a concrete mixture design for shotcrete placement.