The air gap is the distance between magnets in an axial machine, the gap between magnets and stator is a necessary evil to provide mechanical clearance.
A magnetic circuit consists of a magnet, bits of iron and an air gap where the business is done. Iron such as the rotor discs has a low reluctance and needs little in the way of magnet to force flux through. Air is what needs so much magnet to get a decent gap flux, its reluctance is low ( about 1/1000 that of iron). The materials you put in the gap such as resin and copper are essentially non magnetic and behave as air.
Alnico has a much higher remenence than ferrite ( it is similar to neo ) but the coercivity is very low and is easily demagnetised. What defines a magnets usefulness is the BH product and the shape of the demagnetising quadrant of the BH curve. Alnico has a very low BH product. Ferrite is considerably higher and has a straight line demagnetising curve so is much more difficult to demagnetise. Neo has a BH product way higher than ferrite and at low temperatures also has a straight line curve.
Samarium cobalt is not as powerful as neo but not far behind and has a straight line curve up to a few hundred degrees. Being non corrosive it is in many ways the best material to use but has been prohibitively expensive but I see that this is changing.
For conventional iron cored alternators, alnico is not very satisfactory, the stabilised flux level is little more than ferrite, but it may work in air gap machines with a large air gap.
The main reason for replacing Alnico and its many better relatives was the high cost and cobalt shortages pushed the price way up to the point that ferrites were developed (largely for the loudspeaker industry ). It's unlikely you will make a useful machine from Alnico unless you find some big blocks cheap. Mixing alnico with neo is not much use because of the shape of the alnico demagnetising curve, you are adding basically a large air gap to the neo and the end result will be ineffective. Mixing magnets is not really useful but you can get some results with ferrite and neo because the ferrite will run back up its demagnetising curve and not a recoil line as for magnet steels,
Flux