A true hammerhead is an aerobatic, not an air combat maneuver. What you're looking for is the rudder reversal. There are a few reasons for the distinction. The aerobatic hammerhead is done pure vertical and at close to zero airspeed. Pure vertical may be, but isn't always, desired or required in ACM. Also, the slow speed does two things to you. First, it's harder to control and still be able to point your nose effectively until speed builds up on your way back down. Second, and maybe even more importantly, hanging up in the air at near zero airspeed in an air combat environment makes you an ideal target for another NME fighter in the area. You may as well have a neon sign on you that says "SHOOT ME". Another thing to consider is that AH aircraft don't do true aerobatic hammerheads very well but they all can easily do a rudder reversal.
While the rudder reversal can be stretched out to zero airspeed like a hammerhead if you need just a bit more altitude (and you're sure you aren't going to get picked), it's typically done at a higher airspeed while you still have good control. The key is to use yaw to rapidly turn the aircraft 180 degrees (a reversal) from a nose-high attitude and be able to kill the guy below you. As for tips remember a few things.
First, if you fly with Combat Trim on it will tend to add in more and more nose-up trim the slower you go. CT just works off a look-up table and sets trim according to speed, it doesn't care if you're going straight up or level, it'll give you the same trim and that'll make the airplane want to pitch over backward when you're going vertical so you need to either trim manually or hold forward stick to stop the nose at the desired angle.
Next, as you yaw the airplane with rudder, dihedral effect will want to roll the airplane into the yaw (left yaw = left roll). This can work out OK but if you really want a pure 180 then you'll need to use opposite aileron to stop the roll (left yaw = left roll = right stick to counter).
Last, the rudder reversal works best if you do it with the natural torque of the engine so for airplanes with props that rotate clockwise (most of AH's airplanes) you'll want to use left rudder. A few exceptions where right is better are those aircraft with counter-clockwise props like the Typhoon. Another exception are twins like the 38 with two counter-rotating props. The torque produced by the counter-rotating props cancel out so it'll go as easily to the right as to the left. If you want to do the reversal against torque, it's best to cut your power a bit to reduce the torque, especially when flying high-horsepower aircraft.
You last question is easy. Yes, theoretically, a larger rudder makes this easier to do but from a practical point of view all of AH's airplanes will do rudder reversals well.
