They're the original, phase shift keyed modulations.

> Do they actually work well?

They work great, if your problem is SNR, and if you value range more than data rate.

They are, of course, horribly spectrally inefficient which means they work better than OFDM near the guard bands. OFDM has a much flatter power level over frequency, so you have to limit TX power whenever the shoulder of the signal nears the guard band. IIRC, some standard supports individually adjusting the resource unit transmit power which would solve this as well. PSK modulation solves this somewhat accidentally. Guardbands especially suck since there's only 3 non overlapping 2.4GHz channels.

> I don’t think there is anything that low-rate in the current MCS table.

> Do they support modern advancements like LDPC?

Dunno! Generally though, each MCS index will specify both a modulation mechanism (BPSK, OFDM, ...) and a coding rate. All of the newer specs allow you to go almost as slow if you want to, usually 6-7mbps ish , and this is done with the same modulation scheme just a bit faster and with newer coding.

> do those ax resource units work, in practice, in a way that allows two APs that are moderately close to each other to coexist efficiently within the same 20MHz channel?

Yes and no. It doesn't improve RF coexistence directly. But in many cases allows much more efficient use of the available airtime. Before every outgoing packet to a different station consumed a guard interval and the entire channel bandwidth, but now for a single guard interval you can pack as many station's data as will fit.