Unusually high ESR of cheap ceramic capacitors

This unfortunately depends very much on the application. Most low ESR ('low Z'), low voltage (6.3V and lower) electrolytics (e.g. conductive polymer 'solid' capacitors, power supply output filter capacitors) are characterized at 100kHz. Other bulk capacitors (usually 10-63V) which explicitly give ESR in their datasheets are most often characterized at 10kHz. If your application requires knowledge of ESR, this is what you are looking for.

However, general purpose capacitors seldomly have ESR as a statistic in their datasheets. They often only have the loss tangent (tan \$\delta\$) in the datasheet. This is measured most often at 120Hz, but in some cases also at 1kHz. There is usually no use in trying to measure these capacitors at 10 or 100kHz, because the internal construction prioritizes volumetric capacity over impedance, and the ESL makes the capacitors virtually useless at higher frequencies.

And now I'm only talking about aluminum electrolytics - there are many more nuances to this story when you start looking at other build-ups, like metallized film and ceramic capacitors.

So to answer your question: ALL THE FREQUENCIES.

When Q1 turns on there will be a current surge as it discharges capacitors C1 and C1(?). This puts extra stress on the FET and may induce noise into nearby circuits. Using low ESR capacitors will only make it worse.

The 0.1uF and 1uF capacitors you have chosen have a combined ESR of 10Ω||7.5Ω = 4.3Ω, so the peak discharge current will be about 12V/4.3Ω = 2.8A, which should be OK so long as the capacitors are placed close to the FET.

I presume Q3 is low power FET, so its higher on-resistance should limit the surge current in C3.