No, modernization only applies to Staatsmodernisierung. Otherwise you'd say something like Digital- und Staatsmodernisierung. But that would make little sense as Digitalmodernisierung would mean that we already have all the necessary digital processes but they are old and need an overhaul.
A rough translation of Digitales on the other hand would be "things that are digital", which implies that it also includes improving digital processes.
Yes exactly! Like for example Hoch- und Tiefbau. You could still write it out: Hochbau und Tiefbau. But to me that just sounds redundant.