yes it would be illegal to put police on your bike, or to have red + blue lights

I got a ticket once for having blue led's for my wiper fluid ports on my hood of my truck.

I think its a very serious offence too if they were upset enough to bust you for "impersonating a cop" I just got improper safty equipment or some BS not sure what it was. Shame tho they sell them right there in the store and they are illegal to use.

The whole security thing? I dont know if that would really deture anybody from tampering with the bike or not, probably strongly depends on your area. Here with all the punk kids it would be like a homing beacon for trouble I think.

Its the kind of place that if you locked your bike up with a u-lock rear wheel + frame like the sheldon brown method they would steal your front tire.

Best anti theft for a bike I think is besides locking it up correctly and in a good place is to make a expensive bike look cheap. Take off decals, paint over expensive part logos, put tacky reflective tape all over it ect ect... if its a commuter and you keep it outside maybe worth doing.