You're mostly right with the depth of field being the big difference but the image being darker is not a function of aperture (f-stop) directly, but rather overall exposure. At the same ISO setting, two identical shots in the same lighting would be the same brightness with truly equal exposure: the reduction in aperture (increasing to m the f-stop number to a higher value) would be compensated for with an equivalent decrease in shutter speed (in simple terms, constricting the hole lets in less light, so we leave the hole open longer to let in the same amount as before).

In the example, if the scene is darker it's because the exposure changed, not just because of the aperture.

Additionally, the number is shown as a fraction because it is a fraction. The "f" in the value (f/2.8) is a variable that stands for "focal length", that being the focal length of the lens being used. So, for example, a 50mm lens set to f/2 would have its aperture set to a 25mm diameter. (50/2)

The reason the numbers are strange numbers and non-linear in scale is because they correspond to aperture diameters that let in either double or half the amount of light from the stop next to them. So adjusting from f/2 to f/2.8 cuts the amount of light in half (I think this is basically doubling or halving the area of the circle of the aperture).

This is why a one stop change at lower values (bigger openings) has a much smaller numeric shift than a one stop change at higher values: adding or subtracting diameter of a larger circle adds or subtracts much more area than the same diameter change to a smaller circle. That's why one stop goes only from f/2 to f/2.8 on the wide open end, but on the closed down end, one stop goes from f/11 to f/16.

It's not a fraction, it's just the notation used for the aperture setting.

Edit: well, okay yes it is technically a fraction the decimal value is a function of focal length and aperture diameter

Edit: actually ignore me and read the other comment, it's a much more thorough explanation