Here's my interpretation, based on my interactions with TCM practitioners and my understanding of the Chinese language and its approach to communication in general:
Qi is seen as a result of processes, or a state. It is an observed state, and its value is relative to a norm.
If someone has a lot of energy, it is said that they have a lot of qi.
If someone is very nervous, it is said that their qi is rough, unstable, that sort of thing.
If an organ is said to be yang, or having yang qi, that means it is overactive. The opposite is true when it is said to have yin qi.
A "normal" or healthy state is a state of balance between yin and yang, or between overactive and underactive. You know, homeostasis.
Qi is not said to be a mechanism of functioning. It is not a cause, it is seen as a result.
Qi is also a description of the "whatever" that drives bodily function. Martially speaking, when someone says that you should use your qi, they mean that you should not use a specific muscle; you should use your body in such a unified sense (aligned, sensitive and relaxed) that it is difficult for you to sense exactly which muscles you are using. (For example, you can say that you don't use your quads or your calves, you use your legs, but extrapolated, whole body usage says you use your body against the earth.) Since your qi is said to drive the function of the body, and you are using the whole body, you are now using whatever drives the whole body.
Can qi be measured? It can be measured to the extent that energy is measured: only in its physical manifestations that can be detected by our instruments: heat, light, circulation, electrical potential, and so on. Energy, strictly speaking, is not measured: it is calculated based on observations of other phenomena to which instruments respond.
In terms of our bodies, I'd say that it's likely that qi is the result or the effect of electrochemical signals moving through the body and affecting its function. Note the distinction: qi is not the electrochemical signals, it is the effect of those signals.
Qi is a construct, an interpretation, a model, based on observations of phenomena.
That's all I got.