AirRabbit, there are no contradictions in anything I wrote. You are mixing interchangeably what I wrote about
: 1) Circling approach and 2) Visual Approach. You mix "visual" with "visual meteorological conditions". Etc.
You say a visual approach is flown looking out the window. You’ve posted quotes from various sources that indicate that a “circle-to-land” is visually flown from the point in which you reach visual conditions until you land. You’ve also said that you cannot fly a circle-to-land if you have to look out the window. What does that mean?
1) A circling approach is flown in IMC. Runway should be kept in sight, to ensure that you don't leave the protected area.
2) A visual is flown in VMC or at least in conditions that makes is possible to fly the aircraft looking out the window. By flying I mean navigate AND aviate.
Of course a circling may be flown in VMC as well, although it would probably make more sense (economy) to fly a visual approach instead if conditions permit.
Speaking of circling the assumption is of course worst allowable weather conditions. Which are 2400 meter (1.5 miles) visibility and 600 feet cloud base (EU-OPS). Combined with rain, night and turbulence, those are not conditions that permit to aviate the aircraft with reference to outside view, during certain parts of the approach. Like now mentioned a numerous times as example, downwind, flying away from the airport.
You’ve said that on a “Visual approach, anywhere on the approach, the runway might not even be visible.” Is there anything that the pilot must be able to see to fly a “visual approach” or is it just “the ground.” If it is just the ground – is there no particular object on that ground that must be seen?
No, according to EU-OPS there are no particular objects that needs to be seen. I have given following as an example before of one type of Visual Approach that is legal according to EU-OPS:
Airport is covered in fog 800 meter (0.5 miles) visibility. Prior to the airport is a mountain that requires a longwinded approach, that would normally have you fly overhead the field, back outbound and then inbound for an ILS. With mountain clearly visible, you may ask for a visual approach, fly over the mountain and pick up the ILS directly on the other side for a straight in landing on the ILS in the fog.
OPS 1.435 Terminology
“Visual approach”. An approach when either part or all of an instrument approach procedure is not completed and the approach is executed with visual reference to the terrain.
If we intend to fly ... a circle-to-land ... what is it that you expect ... to see when .. you are about to break off from the instrument approach ..? ... If it is the runway and you later lose sight of that runway (which you say may happen) ... now, what do you do? (
Edited for brevity 
)
Yes according to ICAO and EU OPS it is the runway, and nothing else, except object associated with the runway. Like the approach lighting system (no MacDonalds).
I don't think I said that "it may happen", but in that case a go-around is required. If you have doubts about that at this stage in your career, I think really it is time to consider yourself lucky, hang up your spurs and cowboy hat, before something goes terrible wrong. Or wait... was that a condescending rhetorical question?