Electronic – Sizing Flyback Diode

Actually, there's a glimmer of truth in Linards' answer, but not for the reason he thinks.

When your PWM on-time is an odd mutliple of half the powerline's AC period, you are creating a DC component in the current through the transformer. In the worst case, if your duty cycle drops below 5%, you will be putting unipolar pulses through your transformer primary. It isn't going to like this at all.

If you're going to do this kind of AC powerline PWM, you must make sure that your PWM on-times are quantized to whole cycles of the AC waveform, so that there's never any DC component.

If you drop your PWM frequency to 1 Hz, then you can adjust the duty cycle form 0% to 100% in steps of 2% (20 ms).

As for your #2, there is nothing "hard" about choosing the value of the resistor if you understand what is going on.

You take the desired peak voltage across the resistor and divide it by the operating current of the coil. That's it- good old George Simon Ohm's Law. The current immediately after the switch turns 'off' is the same (or a bit less) than it was before, so the voltage the switching device will see is the power supply voltage plus a diode drop plus the operating current times the resistor.

A bipolar TVS could be used in place of the zener + diode if the voltage you wish to clamp at is substantially more than double the power supply voltage. TVS devices are designed to clamp voltage under high current conditions so they're made to withstand massive surges in power (often in the 1kW range). A normal coil doesn't have that kind of surge, so it's a bit of a waste. If you put (say) a 6V bipolar TVS across a 12V coil intending to clamp to 18V, you will have a bad day, since the TVS will conduct in parallel with the coil and probably destroy the driver.

You could use a unipolar 18V TVS across the transistor though.