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1. main switch (SW1) & relay (J3) - is this a common setup? the idea is to connect it to the ignition key which have 3 positions: off, on and reverse.

I suppose at 24V it's ok. Not the reverse part - that's not going to work (see below).

2. Regenerated braking - in case the kart is going downhill and the motor is acting like a generator, the diode D will allow the generating current (mostly in forward but should also work in reverse). Is that o.k.? which diode should I use?

No, diode "D" is already present in the MOSFETs themselves and has nothing to do with braking, whether regenerative or dynamic. Regenerative braking requires changing the converter from the buck to boost configuration which requires a lot more work than what you've drawn. You are pretty close to having dynamic braking, though - just add a resistor for a load (ie - don't short the motor out)

3. Brake - suggested a relay (J4) that will disconnect the motor from the circuit and will short it so it will act as a brake. Will this damage the motor?

You need to insert a load resistance otherwise, yes, you will damage the motor (and probably the relay, too). Keep in mind the resistor will need to be capable of handling the peak current and power expected. Since this is a small motor you could probably get away with a bank of cement-filled resistors (5W to 10W) that comes out to around 0.5 to 1 ohm and at least 50W (the peak power handling capacity for a few seconds will be at least 4x that amount).

 

[Tesseract]

Do you mean the reversing circuit will not work? that part already exists and reversing the motor well.

Sorry - I was thinking of regeneration when I wrote that.