Chicken6 me'old, you take me back to the depths of my CFS groundschool a few moons ago. I will do my best to answer your questions in simple terms as that is all I work in.
First the requirements of a max rate turn are;
1. C/L max, i.e highest possible AOA without stalling which means the light buffet.
2. Max AoB, the more bank, the higher your rate of turn.
3. Full power, more power means more speed, more speed means more g for any given AOA, more g means smaller radius / higher rate of turn.
4. Low altitude, the lower you are the more power your engine will produce and the lower you are the thicker the air is hence more lift for a given AOA. Think about the equation for lift, Lift = 1/2*Rho*Vsquared*Cl*Wing area.
To your questions;
1. I can't remember off hand what flap will do to the rate but it is really irrelevent as most a/c dont have flaps stressed to more than 2g and trying it with flap will simply overstress the a/c either in g or in IAS.
2. See point 3 above.
1b. Radius is affected by g and IAS at the time which often vary as the a/c slows down. Also radius is not important, rate is. More rate means you can turn faster (more degrees/sec) than the other guy so you can get on his tail and not vice versa. Guns Guns Guns!!!!!!!!
3. Gengis answered that one.
4. Again Gengis speaks the truth. Basically its the top of the hill without going too far and down the other side.
Hope this has helped you out and Merry Christmas all. My head has just exploded. Principles of Flight and hangover dont mix.
Doh!!!!!!!!!!!!!!!!!!!!!!!!!!!!