Feedback schematic/pcb 16 channel relay wifi module
Excellent question technique.

Probably.  I'm not familiar with the ESP device, but everything else looks good.

No.

I would add a 10 uF electrolytic in parallel with C8 and C9.

Yes.

Yes.  If the size is an issue, reduce C4 to 100 uF and distribute 100 uF caps near the relays.  One cap per relay will be a lower total capacitance but will have much better response to coil transients.

Yes.