1. Yes you can wire your inputs with external 24vdc supply. However, "Y" ports are outputs, not inputs. Inputs are "X". See page 12 figure 10 (a). You need to use inputs X310-315.
2. I think I read on a forum / thread somewhere that a diode is recommended. In practice, I have used the outputs to control relays similar to the one linked without adverse effect.
3. My machines are different, as I float the 0VDC. So the probe is a simple switch (NPN) to the mentioned input. Have you checked to see if the spindle shaft has continuity to ground. Sometimes the shaft is isolated because of the bearings. I would think that if the bit has continuity you may have to devise an alternative method.
4. If I understand correctly you are describing a star ground, so yes. All grounds to one location, shortest path possible and then to earth.