My third question is about what kind of load is the screen grid on power on? Is it of a capacitive nature?
In your schematic:
1. Why do you use diodes after the transistor? In which situation can happen that current flows in the opposite direction?
2. Why do you use 22uF on the gate, for filtering reasons? and why is a diode there?
The screen grid has very low capacitance and is of no consequence at power-up. The usual filter capacitor associated with the screen grid is of great importance concerning the inrush current at power-up, however. There is no filter capacitor at the screen power node in my schematic and there is a 10K current-limiting resistor in series with the P.I. filter capacitor, so inrush current through Q1 is not an issue. Accordingly, I have removed the 10R/12V zener current-limiting network.
1. Consider the case when the standby switch is first connected to ground. There is no Gate current, so the Gate is at 0V. C4 is at 400V, so the Gate-Source voltage would initially be 400V without D2. The STP6NK90Z has internal zeners to protect the Gate-Source junction, but using a feature that is meant for emergency protection as an integral part of the power supply design seems like poor form to me. Also, the STP6NK90Z is way overkill for this application and somebody might just substitute in a lessor part with no internal protection.
D3 prevents the lingering charge on C5 and C6 from energizing the screen grids when the standby is connected to ground. This way the standby takes full effect quickly.
2. The capacitance on the Gate gets multiplied by the gain of Q1 when it appears at the Source. This way the filtering for the screen node is way more than if C3 had been placed at the Source, instead.
If you turn the power off, the still hot plates will drain C1 and C2 rapidly and bring the Drain of Q1 towards 0V. If the Standby switch is in "play" mode, C3 will discharge relatively slowly. This will result in the Gate becoming positive with respect to the Drain. I don't want the Gate positive with respect to the Drain, so I put D1 in to prevent this.