What really is a fluid? My question may be pretty basic, but I feel it is important to ask this as I've gone through several texts and none offer me the clarity I seek.
The question is: What is a fluid? What is flow? If we say that a fluid is something that flows, the next right question to ask would be what flow is. To my surprise and disappointment, there is no clear distinction between various definitions, which I present in the form of questions - 


*

*Is a fluid simply something that can flow?

*Is a fluid, an object that can be continuously deformed, as a result of shear forces? (fluids can't sustain tangential stress)

*What is flow? Does it refer to the motion of fluid elements relative to one another, or does it refer to the motion of the fluid as a whole with respect to the container it is contained in? or, is it just the continuous sliding/deformation of fluid layers, which texts refer to as flow?


So, what properties really define a fluid? (Something that brings up a clear distinction between fluids and non-fluids) 
A detailed explanation would be great. Thanks a lot. 
 A: There is no standard definition of the word fluid. It is a somewhat imprecise term used in various ways by different people.
Indeed, in real life there is no simple example of a fluid. There is a spectrum from superfluids at one end, through non-Newtonian fluids all the way to crystalline solids. I speak as an (ex) industrial colloid scientist who has spent many happy hours studying the flow properties of many vaguely fluid systems.
The practical definition widely used by colloid scientists is that a fluid is something that has a measurable viscosity. That is, if subject to a constant shear stress (typically in a rheometer) it has a constant strain rate (note that non-Newtonian fluids may take a long time to equilibrate to a constant strain rate).
The problem with this is that if you carry out your measurement for long enough even apparently solid materials like pitch will flow. I have heard rheologists claim that on a long enough timescale everything is fluid, though these claims tend to be reserved for the bar rather than in refereed publications. Where you draw the line between a fluid and a solid depends on the application and to an extent personal preference.
A: Before Einstein's 1905 paper "Investigations on the Theory of the Brownian Movement" many physicists and even chemists didn't believe that molecules or atoms really existed.  A fluid was considered a fundamental object. We now know that all fluids are really aggregations of particles. At temperatures above 0°C these particles are in constant chaotic motion. It is called Brownian motion after the botanist Robert Brown (born 1773) who, under a microscope, noticed a ceaseless movement of pollen grains in water.  A fluid is said to be flowing if, in some reference frame, the particles' velocity vectors all have large components in the same direction. All the characteristics of the fluid, temperature, flow velocity, shear stress, viscosity, density, all are due to the motion of the particles.  In some situations the particle nature of the fluid can be ignored.  This is when the "fluid approximation" is valid.  This approximation ignores viscosity and indeed any interactions between the particles. In other situations this approximation is not valid.
A: Of course fluids have been around for longer than we humans have. Our usual and historical encounters with fluids are at our, macroscopic, level. Although Democritus spoke of them, atoms were not the stuff of physical thought until Einstein’s 1905 paper explaining Brownian motion. This was the first proof of the actual physical existence of submicroscopic particles. In this paper Einstein showed that fluids were indeed collections of interacting particles. Before that, Mendeleev’s chart of the elements was only thought of as a formal bookkeeping method for chemists. The elegant mathematics of fluid mechanics was and is very attractive but now it had to be shoehorned into the reality of the existence of atoms and molecules. It is for this reason that fluid mechanics texts preface their treatment of fluids with the “fluid approximation,” i.e., that fluids are really made up of molecules and atoms but that this fact will be put aside. This approximation ignores particle-particle interactions and it ignores the interactions of fluid particles with solid surfaces. Viscosity, a macroscopic property, is introduced to account for these.
In keeping with the view before 1905, then, a fluid was defined as a substance that takes the shape of its container and that does not exhibit static shear strain, i.e., it does not deform statically. Of course vortices and whirlpools and their attendant distortions of the fluid’s surface were observed but these are dynamic strains. Except for viscosity, then, a fluid was approximately ideal. An ideal fluid is one in which there are no particle-particle interactions. The effects of particle-particle and interactions between the fluid particles and solid surfaces in the flow are supposedly accounted for by the introduction of the notion of viscosity. This keeps the fluid approximation intact. There still are problems, though, in explaining some fluid behaviors, for example consider Bernoulli’s principle.
The principle is illustrated by the behavior of a fluid in a Venturi tube. A gas at a fixed pressure in a large container is allowed to exit through a narrow tube. In this tube Bernoulli’s principle relates the velocity of the exiting fluid to the difference in pressure between the large container and exit tube. At the macroscopic level the force that accelerates the fluid from zero in the container to its exit tube velocity is due to the pressure difference between that of the container and the final pressure of the space into which the fluid flows. This is all fine until one considers the manometer that measures the pressure differences. The flow rate of a real, i.e., viscous fluid at the walls of the apparatus is zero. How, then, do the manometers work, since they are installed in the walls? How is it that they measure the flow rates? The problem is that the fluid approximation is not valid at the walls.
What is going on at the particle level? What the manometers are sensing is the pressure due to the collective effect of the components of the velocities of the particles normal to the wall. The orifice into the exit tube is a sorting mechanism. Evidently only those particles which are at the orifice and whose velocity vectors are directed into the tube contribute to the flow in the tube. The particles whose velocity vectors are not precisely normal to the area of the orifice will strike the wall of the exit tube. Within the exit tube, of course, there will be particle-particle collisions but the average motion of the molecules will be in the direction of the tube. The fact that energy is conserved is reflected in the fact that the collectively increased velocity of the particles in the direction of the tube’s axis is accompanied by lower velocity components normal to the walls than the average within the container from which they came. This is what the manometer senses. This is why the pressure of the fluid in the exit tube is lower than that of the container. The exit tube’s orifice is a selection mechanism, like Maxwell’s Dæmon.
A: Fluid is essentially a summary category for liquid + gas. And that makes sense, because an incompressible gas obeys the same equations of motion as a liquid. Hence, the term "fluid dynamics" applies to both. As one goes into greater detail, there surely are ambiguities; in particular we could discuss forever the difference between a liquid and a solid. Non-fluids are solids. 
