Electronic – Does low power in the mains causes damage to household supplies

Seems like you want to get the max power from the resistors and power supplies that you've got. 3D printing is a long process. I don't see how temporarily exceeding the rated power dissipation can help. The following is for the steady state.

12x 1Ω resistors, each rated for 10W. The max steady state overall power you can dissipate is 120W. Each resistor dissipates \$P = I^2R\$. The max rated power is reached when

\$I=\sqrt{\dfrac {P_{rated}} R}=3.16A \approx 3A \$

Pick a series/parallel combination of resistors such that

\$\dfrac {V_{supply}} {R_{series}} \approx 3A\$ (just under 3A)

This can be achieved by using the 12V power supply and resistors in 3x parallel strings each with 4x resistors in series. Each string will pull 3A. Together, all 3x strings will pull 9A. The 12V power supply in the O.P. is rated for 18A. It should be able to supply the current.

Construction tips

• Use thermal grease
• Thermally insulate the bottom of the plate, if possible.

Are you trying to emulate a power button press to turn on a computer, or do you just want to turn on the power supply by itself?

For emulating a button press, I would recommend either a relay or an optoisolator. I don't think there are any standards for how the power button on the motherboard is set up, so it would not be advisable to rely on, say, one of the pins being ground.

For turning on the power supply, all you need to do is tie the PS_ON signal to ground. This signal must be held low to keep the power supply on. Since this is a well-defined standard, you can use a single NPN transistor to pull that pin low under the control of a microcontroller or similar.