Electronic – How to monitor this AC circuit

Obvious problems: Well yes. As drawn right now, there is some confusion but:

1: Either you don't get 220V to your secondary relay (The one connected to the Arduino) because the line leaving your primary relay going left is a trigger signal line, rather than a power line OR

2: You DO get 220V to your secondary relay and you cannot trigger your first relay because the line leaving your primary relay going left is a power line, rather than a trigger signal line.

My first recommendation would be to redraw your diagram with clear labels on all wires.

If you have access to the ground (more accurately, negative) side of the load, you could probably use a smaller N-channel FET than the P-channel that you have because of the way that FETs work. Something like this:

^{simulate this circuit – Schematic created using CircuitLab}

Don't forget D1, regardless of how you control it. It limits the voltage spike when turning off to a diode drop above the supply by providing a path for current to continue flowing through the inductive load for a (short) while.

If you must control the positive side, then your PFET circuit looks good, except that your R18 is 220 ohms with 12V across it when the motor is on, which comes out to 0.65 watts. With that value, I would not go any less than 1 watt, but you should probably look at a higher value instead.