You can often make educated guesses, but not every detail can be known from the final image alone.

For portraits, start with the light: look at shadow direction, shadow hardness/softness, catchlights in the eyes, and how evenly the face is lit. Those clues often help you tell whether added light was used and whether it was likely on-camera or off-camera. On-camera light tends to look flatter and more frontal; off-camera light usually creates more obvious modeling and directional shadows.

Aperture and shutter speed are much harder to determine precisely unless you know other variables. What matters more is the visible depth of field and any motion blur. In portraits, depth of field is usually the most useful clue for estimating aperture range.

Reflectors can sometimes be inferred from gentle fill on the shadow side of the face or additional catchlights, but it is often difficult to be certain. Distinguishing silver from gold is especially uncertain unless the fill has a clearly cool/neutral or warm color cast.

In short: reverse-engineering is mostly about reading light quality, direction, and depth of field, then making approximate rather than exact conclusions.