Identifying food, quick and cheap? I’m asking this question in the most technical perspective of identifying substances, so I’m not considering the use of chemical tests like Benedict’s solution, biuret solution, Sudan III stain, or indicator dichlorophenolindophenol, as valid answers since these methods rely on identifying the color by observation. The answers I’m really looking for are based less on physical and more on chemical properties without the need of human observation or intervention. 

(At this point, if you have an answer please reply… the rest is clarification to my question)
With that being said spectroscopy, chromatography, electrophoresis, and biochemical analysis are more along the lines of the answers I’m expecting. However, I’m really asking which of these methods or others in connection with other techniques, are the most convenient, smallest in size (in terms of equipment), and cost-effective in identifying food sources. 

So in attempt to sum up my question, here's a scenario: I have a yellow onion. I extract juice from the onion and I give it to a skilled chemist/engineer labeled unknown. Using an analytical technique, in about a few seconds, the chemist supplies a prediction based on the components found within the unknown food (amino acids, peptides, proteins, enzymes, lipids, phospholipids, carbohydrates, alcohols, fat-soluble vitamins, water-soluble vitamins, organic acids, organic bases, phenolic compounds, bittering substances, pigments, aroma compounds, and dietary fiber) 

What is/are the analytical techniques used? Is there a device that does such a thing?
Unfortunately, your confidence in what a chemist can, is quite exaggerated. Though flattering.

Analyzing the entire range of parameters that you list, requires several analytical techniques, including sample preparations like homogenization, extraction etc.

A technique like Near-infrared spectroscopy can give an easy and fairly good estimate of some major components (protein, fat etc) in selected types of food. FOSS Analytical (and probably several others) purchases equipment for this.

Routine methods exist for analyzing components like vitamins, pigments or metals, but they require a laboratory setup and often very expensive equipment.