Quote:1- Changing the elevator usually causes a delayed response, the change I make now might be good enough to achieve the expected rate of climb but that will only be reflected later.

The delayed response from the elevator is typically well-established, and can be taken into account by the augmented control system that exists between the hardware and the autopilot. The time constant for the elevator itself will be fairly small for most systems compared to the movement of the airplane, so I wouldn't worry about this too much.

Quote:2- In most aircraft you need to follow a very specific climb rate in feet per minute, (fpm), rather than aiming for a certain altitude.

Consider the following phases of a climb:
- From a level flight path, the aircraft establishes the desired altitude.
- The aircraft begins to change pitch in order to match the desired rate of ascent / descent. Call this rate P_r (pitch rate).
- The aircraft establishes the desired pitch angle (A_p) and ascends / descends towards the desired altitude.
- The aircraft approaches the desired altitude within a known margin, at which point P_r is reversed, although this time it is scaled in proportion to the difference between current and desired elevation.
- A pitch angle reaches zero. Small angle adjustments, with large time constants (heavily damped) to avoid overshooting, are made by a separate or reduced control system.

The two keys to the above algorithm are:
- P_r, which is unique to a given airplane and is determined by airplane performance ability and the maximum allowable moment arm about the pitch axis. (If you're in a commercial airliner, P_r should be small, since you can only change angle so fast while keeping your passengers comfortable.) A_p is determined by P_r (ie, how fast will you be able to pull out of a steep climb?).
- In the fourth phase, note that the control system attempts to predict when it should start pulling out of the climb. You can do this by:
a) extrapolating the current time-to-altitude from the rate of descent and attempting to solve the resulting differential equation (keep in mind that your rate of decent changes as you pull out of your climb / descent)
b) pick a set distance (say, any altitude within 500 feet of the desired altitude) and trust your corrections in phase 5 to compensate for any difference

One thing that a realistic simulation or control system must take into account is the fact that A_p and P_r will change as a function of altitude - your elevator will apply a different moment at the same angle, depending on the surrounding air pressure.

Good luck!