What distinguishes "individuals"?
Disclaimer: the following answer is based mainly on the ideas of empiricism (Locke, Hume, Berkeley, Kant), it is just a logical consequence of such ideas, and are part of the book I'm currently writing, related to the theory of systems, so, no punctual references.
The distinction is purely mental (essentially, Berkeley). The universe is constant change. So, a river is not the same river a second ago. Same happens with a rock or the person you saw on the mirror the day before. Reason is the mechanism that makes subjectively possible assessing objective change as static things. In other words, the mind models change as static objects. The thresholds (where are the limits of trees, clouds, rocks, persons, houses or football teams) are always the result of subjective mechanisms (perception and reason determines what you know; otherwise there's no independent truth regarding what are the limits of a mountain: any independent truth must be universal, so it should apply even to aliens).
There's no physical correspondence between an apple and a number. The number is an abstraction of the thing. Strictly, two apples (total=2a) would be possible only if they are absolutely identical in all forms, otherwise they add as total=1a+1b. It is your mind that provides the boundary between what is and what is not an apple.
Regarding the distinction macro-micro: in thermodynamics, macrostates are dependent on perception (e.g. temperature is essentially a feeling), while microstates are not (we do not perceive the state of individual particles, or the composition of the system, whatever the microstatic perspective we select). Such approach is coherent with the previous one.
Nothing but habit and common sense distinguish individual objects.
The whole "table is mostly empty space" thing is misleading because "empty space" and "particles" don't really fit with modern physics. There are just fields on spacetime, which interact with observation and experiment in ways that seem particle-y sometimes.
In Physics, the strictly distinguishable "individuals" we know are the different elementary particles (fields); we distinguish, for example, particles with electric charge from neutral particles. In this fundamental sense, only a few "individuals" (electron, muon, tau, photon, up quark, ...) constitute the known universe (instances of the same particle are not distinguishable).
But this is just the most fundamental theory (and distinction) we have. At larger scales we distinguish atomic spieces, materials, apples, people - DNA tests are quite accurate.
Quantum mechanics has many different interpretations. One, which is commonly accepted, is called Copenhagen interpretation. This idea says that an electron is everywhere at the same time but the probability to find it at some point in space by a measurement is its wavefunction modulus squared. Note that the electron is everywhere at the same time. In other words, there is no boundary. We distinguish between phenomena based on our previous experiences and those "individuals" are just mental constructs. Therefore, the answer to the question that what distinguishes between phenomena (like Earth and Mars) is actually the mind! In fact, every electron in Mars is on earth at the same time and the same is true in the other way around. (Other questions you have asked about intermolecular forces are outside the boundaries of philosophy).