The first question is the ratio in between the number of poles and the number of coils. First you have to understand this for a 1-phase winding and then for a 3-phase winding.
Assume that the armature has 8 poles and that you have a 1-phase winding. Then you need four coils. Each coil has two radial legs. The two radial legs are connected to each other by an inner and an outer coil head. The coil must have such a shape that, if the left leg is opposite to a north pole, the right leg is opposite to a south pole. The voltage generated in the left leg is then in phase to the voltage generated in the right leg and both voltages are strengthening each other maximally. An 8-pole armature has the same magnetic position if it has rotated 90°. So a rotational angle of 90° corresponds to a phase angle of the generated voltage of 360°.
Next assume that you want a 3-phase winding. This means that there must be a phase angle of 120° in between the phases. This angle corresponds to a rotational angle of 30°. Assume that the three phases are called U, V and W. So the coil pattern of the coils of phase V has to be rotated 30° with respect to the coil pattern of the coils of phase U. The coil pattern of the coils of phase W has to be rotated 60° in the same direction with respect to the coil pattern of the coils of phase U. This rule is right if all coils have the same winding direction. Changing the winding direction from left hand to right hand results in a shift of the phase angle of 180°.
So you have totally 12 coils for an 8-pole generator. If you lay the four coils of phase U first, then the four coils of phase V and then the four coils of phase W, you get a 3-layers winding with a lot of crossing coil heads. Mostly the 12 coils are not laid this way. Normally one uses a 2-layers winding in which first six coils are laid in the sequence U1, V1, W1, U2, V2, W2. There are no crossing coil heads of the six coils in this first layer. Then a second layer is laid with the coils U3, V3, W3, U4, V4, W4. There are also no crossing coil heads for the six coils in this second layer
The disadvantage of a 2-layers winding is that you get crossing coil heads for the coils in the first and the second layer. So for most axial flux generators, the second layer is cancelled. So you have only one layer with the coils U1, V1, W1, U2, V2, W2. But this means that twelve possible positions for radial wires are not used. The coil figuration for a 1-layer, 3-phase winding is given in figure 9 of my report KD 341 for an 8-pole axial flux generator with rectangular magnets. The upper picture gives the ideal coil shape. The lower picture gives a shape with a larger thickness of the coil bundle. So if you have understood this explanation you can use a similar theory if the armature has more than eight poles. A 1-layer of 2-layers 3-phase winding is only possible if the number of armature poles is dividable by four, so if the number of poles is 8, 12, 16, 20 and so on.
Your question about matching can't be explained on a simple level because you must understand the rotor formulas first. Matching is explained in chapter 8 of my report KD 35 (available in English and in Dutch). Perfect matching means the the generator is loaded such that the rotor runs at its design tip speed ratio and so at the point of the Cp-lambda curve for which the Cp is maximal.
