The L2 and L3 windings are short-circuited in your schematic.
The inductance of a transfomer winding varies as the square of the number of turns. So for a transformer with a 5.75:1 voltage ratio the inductance ratio of the windings will be 5.75^2:1 = 33.1:1.
Do you know the winding inductances...
It's above my pay-scale, with all those Amps. It will need serious engineering and possibly critical layout, taking onto account heat-sinking, back-emf and EMI.
The resistors in my posted circuit have nominal values and are there only for the purpose of the simulation. The 1 Ohm represents inherent coil resistance and the 100 Ohm represents an arbitrary load resistance. Omit them in a real-world circuit.
Theoretical current draw at the rated output is 114A. Peak (start-up/stalled) current will be greater, probably a good bit greater. You'll need a hefty PWM controller! Also a good battery.
That sounds right. If your meter (set to measure Volts) doesn't have a centre-zero then the needle will either hit (or stay at) the left end stop, or else it should move to the right a bit. Just ensure the same magnet polarity and the same approach direction are used for each coil in turn.
Easy to make a primitive one. Place a magnet (or magnetised needle) on a bit of polystyrene foam and float it in a cup of water. Or hang a magnetised needle on a cotton thread.
As a N pole approaches a coil there will be one coil polarity. As the N pole moves away from the coil the coil polarity will reverse.
Something like this.