A model transmitter has "line of sight" range. The limiting factor is what the pilot can see. So after a few hundred yards it becomes v difficult. early drone systems used binoculars on stands so that the pilot controlled them whilst viewing through the binos. Now we have "first person view" systems where there is a small camera mounted on the model sending a video pic back to the pilot who wears a set of VR goggles: he sees what we see and flies accordingly.
Those Anti crash systems work poorly at best, at night I doubt they'd do anything: but it matters not, a good RC pilot wouldnt need the system even at night.
A model would easily chase a helo, but probably more by accident than design.
I suspect that the police chopper would outrun the model in seconds - it would be pretty hard for a model pilot to circle it and keep up, especially at night. The helo wake would seriously affect the model IMHO. Big bals models fl;y quickly but those lightweight foamies, whilst they have very high power:weight ratios, fly slowly.
David
BMFA Instructor