I am not sure why you chose 15 coils.
It will no doubt work but you will have a high phase number and will need to wind each coil with a lot of turns and you will need a diode pair for each lead.
The normal 3 phase arrangement will be 18 coils for 24 magnets.
Unless there is some reason why you can't ,I would be tempted to space the magnets more to reduce leakage flux and give you more winding area to use thicker wire.
A spacing equal to magnet width at the centre would help you to produce more from your limited magnet supply.
The hole in the coil should be the size of the magnet, but make the legs wide enough for the coils to touch at the inside diameter.
I don't think there is any benefit making the coils trapezoidal over rectangular, the flux linkage is the same and the trapezoidal coils have more resistance.
I assume your magnets will not be an ideal rectangle, so if the magnets happen to be wider at the outside then trapezoidal coils may be better.
Flux