(Fade is not as much as the pads getting hot but brake fluid reaching boiling point.)
not true. Fade is hot gasses building up between pads and disc usually due to repeated hard stopping. Hit the pedal and u get little friction
boiling fluid is also due to overheating or sometimes air in the lines or both. When u hit the pedal the pedal goes to the floor
Partially true. Brake pad out-gassing is a phenomenon that hasn't been an issue since the 70's, which is when brake pad friction material consisted of only organic compounds. With the advent of semi-metallic and and ceramic brake pads with modern compounds, brake pad out-gassing was no longer an issue.
In regards to brake pad induced fade, this still occurs but for a different reason. Every brake pad, regardless of composition, has a specific friction co-efficient that is temperature dependent. A typical OE semi-metallic or ceramic pad in a non-high performance application will exhibit good "bite" (high friction co-efficient) when cold and during normal use, but under track conditions the friction co-efficient will decline as the pads become hotter. This requires more brake pedal effort and travel to slow or stop the vehicle.
On the opposite side of the spectrum is brake pads that are designed for race applications. They squeal badly and stop poorly when cold (street driving), but as they heat up they bite harder and can withstand extreme temperatures without fade. They tend to be very rough on the brake rotors.
As far as fluid reaching the boiling point, this can certainly cause the brake pedal to fade severely. Brake fluid is glycol based (except for DOT5, which is silicone) and absorbs water over time, even in system that hasn't been opened. The more water that is absorbed, the lower the brake fluid boiling point becomes. When the fluid boils, it changes from a liquid to a gas (air). As you mentioned, air in the lines can significantly increase brake pedal travel or result in a complete loss of brake function.