I The pattern of one photon at a time passing through large-distance setups?

[jtbell]

For a single slit, 3 cm might already be too large to get significant diffraction effects with visible light, since it is about a hundred thousand times larger than the wavelength.

A very wide single slit is simply two instances of edge diffraction, facing each other. If you move the edges closer together, the two edge-diffraction patterns merge in a complicated way. The result has to be calculated using the methods of Fresnel diffraction. When the slit becomes narrow enough, you get the familiar simple single-slit pattern of Fraunhofer diffraction.

 

[tade]

Then you won't see an interference pattern on the detector.No. You still won't see an interference pattern on the detector.See above.

and also, regarding the "bundle of pencils", I'd just like to ask, what are your thoughts on the simplified notion (if I am hopefully allowed to mention this notion, for the purposes of trying to cover the scenario more comprehensively) that making it a "full gushing waterfall" will enable the wave(function)s of the multiple "pencils" to blend together, and thereby resulting in an overall larger "effective width"

So I understand that you've said on this "See above.", relating to the prior answers, though from my perspective, what I'm adding might be a new different line of reasoning, or approaching the scenario from a different viewpoint

 

[PeterDonis]

what are your thoughts on the simplified notion (if I am hopefully allowed to mention this notion, for the purposes of trying to cover the scenario more comprehensively) that making it a "full gushing waterfall" will enable the wave(function)s of the multiple "pencils" to blend together, and thereby resulting in an overall larger "effective width"

I've already told you: that's not how it works.

from my perspective, what I'm adding might be a new different line of reasoning, or approaching the scenario from a different viewpoint

Your perspective is flawed.

You should be spending your time and effort learning the math of QM and how it is used to make predictions. You should not be spending your time trying to dream up ever more elaborate scenarios that are just going to be flawed because you don't understand how QM works. That is not a good use of your time, and it's not a good use of the time of the posters here who are responding to you.