Just to start off, I am a Military Cop. I am nationally RADAR/LASER certified.
1.) No, a radar detector is not illegal in the state of California. Local laws may vary in other states, though.
2.) A cop cannot pull you over for having a RADAR detector. But, having one is telling the cop that you have a problem with speeding. So be careful.
3.) No, a cop cannot write you a ticket for having a RADAR detector.
4.) Accuracy depends on so many things. It depends on weather conditions, wether or not the cop is even using RADAR, and how well the unit is made. My RADAR detector cost me $250 last year. It is a really good one for the price. It can detect a cop using Radar approx 3/4 mile away.
Above all, a few things to remember:
A.) Radar is 300 feet wide at 1000 feet distance.
Laser is only 3 feet at the same distance.
B.) Laser has unlimited range. It is light. There is no beating it.
C.) ALWAYS BE AWARE OF WHATS AROUND YOU!! That and not speeding are the things that will keep you out of a ticket. If you see a string of cars start hitting their brakes or stacking up with a nice open road in front of them, be aware. There may be a cop up ahead.