Electronic – Sourcing parts for Really, Really low frequency filters

It's a low-pass filter which attenuates high-frequency signals and allows low-frequency signals to pass through it. Basically, the capacitors pass high frequencies better than low frequencies so high frequencies are shunted to ground, and don't appear on the output. The inductor works in the opposite fashion, and passes low-frequency signals much better than high-frequency ones.

If you find the theory behind that type of filter difficult, make one for yourself and try it out with a suitable signal generator and oscilloscope.

Where I once worked, I designed a system that met all the EMC requirements in our preliminary testing, apart from a VHF emission from the RS-232 cables that connected it to the host PC. An additional little PCB by the RS-232 connector with Pi filters as in that article solved the problem and the system passed the formal tests without any problems.

This is hard to answer without knowing the what exactly is going on inside the control loop, which is probably not described with much detail in the datasheet. Saying it is "optimized" for 30 mΩ doesn't say what it really needs or what happens when it's not exactly 30 mΩ. Since they make a issue of the output cap ESR, there should be a min/max ESR spec elsewhere in the datasheet.

Hopefully 0 ESR is OK, else it gets inconvenient. Lower ESR is generally better, and certainly closer to ideal, for a capacitor. Capacitor spec sheets therefore often only spec maximum ESR. In that case you either have to get the guaranteed minimum from the capacitor manufacturer, or add deliberate resistance. A better answer is to stay away from chips that specify a minimum output cap ESR to be stable.

That chip is probably old, as ceramic capacitors have come a long way in the last few years. These have much lower ESR than tantalum, and can now approach such capacitances at reasonable cost. Newer chips now make use of the lower available ESR to get better performance instead of requiring the capacitor to have a high resistance. This is a all around better strategy.