Is it true that NCPD only investigates large-scale and cant-sweep-under-rug crimes?
Yes and no. From the Night City Sourcebook, (because I cannot find my copy of Serve and Protect): NCPD is underfunded and under-manned, but they do regular police work. Much of it is conducted by drones and camera surveillance, but if you commit a drive-by in front of NCPD, expect trouble. Likewise, if a crime involves someone connected to or useful to the NCPD or City Hall, expect an investigation. The only crimes to typically get -full- police attention are the crimes you mentioned, yes. The Police do have callboxes on many streetcorners.
Is it true that there is an EXTREME college campus security force and incorruptible harbor police force?
I have the distinct feeling you know the answers to these questions...anyway, yes and yes. The Harbour Police are notoriously incorruptible hard-asses. There are probably exceptions - good luck finding one. The "Mad Maxes" of NCU are also very short with troublemakers - interestingly enough, students can enter an agreement with the NCU Campus Police for protection off-campus, if they live nearby.