I'm not a competent engineer yet but since there is no answer to this important question I will answer. Don't rely on me %100 and go watch these videos for the topic:
Understanding the Basics of a Flyback Converter - TI training
Flyback : Quasi Resonant (QR) Mode
Flyback : Valley Switching Mode
Valley switching and Quasi resonant are similar DCM methods but not exactly the same thing. Valley switching mode can turn on the MOSFET on different valleys where Quasi resonant switches the MOSFET on the first valley only. For a fixed duty ratio, Valley Switching (aka frequency foldback) mode controller will behave as below:
For light loads the controller will wait longer (skip more valleys) before turning on the MOSFET. This will cause increased period thus low switching frequency. On heavy loads, valley switching mode controller will turn on the MOSFET on the first few valleys or even in the first valley (which turns it into a quasi resonant converter just for that specific operation point), this will shorten the period thus increase switching frequency. This mode of control is called "frequency modulation (FM)". To my understanding, although valley switching converters can work on different duty cycles it is like changing gears. Basically there are few different fixed duty cycle modes for a few ranges of output power. For your third question I would say: If the converter were to skip less valleys on light loads for the same peak primary current that would increase the output voltage over the required.
There is also amplitude modulation (AM) which controls the peak amplitude of primary current. It is basically adjusting the duty cycle. Since the Quasi resonant converter has to switch in the first valley, it is not completely free to adjust switching frequency. It has to control the duty cycle in order to regulate output voltage. When the load increases, the duty cycle increases and demagnetization time also increases, this pushes the first valley which occurs in the dead time forward thus creates a bigger duration until the turn on of MOSFET. That's why switching frequency decreases with the increase in load. Since the duty cycle is changing, the first valley occurs on different times and the controller needs to adjust the switching moment which means adjusting the switching frequency. Thus, Quasi resonant converters implement both FM and AM and have higher efficiency but are also harder to control.
