Why the image is upside down. Light travels in straight lines. A ray leaving the top of a tree and passing through the hole must continue in a straight line, so it lands low on the screen; a ray from the base lands high. The image inverts because the rays cross at the aperture. Everything else about the device follows from that one fact.

The trade-off you just measured. A smaller hole means each object point maps to a smaller patch on the screen, so the image is sharper — but less light gets through, so it is dimmer. Shrink the hole too far and diffraction, the bending of light at an edge, spreads the light out again and sharpness gets worse. There is an optimum, and every camera aperture since is a negotiation with the same three-way trade between sharpness, brightness and diffraction.

Ibn al-Haytham. The first full scientific explanation of the effect came from Ibn al-Haytham (c. 965–1039), the Arab physicist known in Latin as Alhazen, who showed how light entering a dark room through a small opening produces a sharp inverted image. The phenomenon had been noticed earlier; the explanation is his, and it is one of the foundations of optics as an experimental science.

Adding the lens — get the credit right. The lens is a Renaissance addition and the sequence is often muddled. Girolamo Cardano documented a convex glass lens in the opening of a darkened chamber in 1551. Giambattista della Porta described using a concave mirror to project the image as a drawing aid in his Magia Naturalis of 1558 and did much to popularise the device. Daniele Barbaro, in La pratica della perspettiva of 1568, recommended a biconvex lens made from spectacle glass, discussed adjusting the lens-to-screen distance for focus, and added an adjustable diaphragm — an aperture control. Della Porta is frequently credited with the lens; he was not first.

The artist's tool argument. Once you have added the mirror in step 11 you have a tracing device, and whether painters used one is a live and sometimes heated art-historical debate — Vermeer's name comes up most often. The honest position is that the technology plainly existed and was described as a drawing aid, while proving that a specific painting was made with one is very hard. Build it, trace with it, and you will at least understand what the argument is about.

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