Excellent question! The two major types of bonding in compounds are covalent and ionic bonds. In the covalent bond, electrons are shared between two (or more) atoms, which creates a bond that links these atoms. For instance in water, H₂O, the electrons are shared between the two hydrogens and the oxygen. The oxygen is more electronegative and thus has a slightly negative polarity. On the other hand, in the ionic bond the electrons are largely isolated to the more electronegative atom. For instance in NaCl salt, the chloride ion Cl- takes the electron from the metal sodium ion Na+. As a result the electrostatic interaction between a positive and negative ions creates this ionic bond. Generally ionic bonds are stronger than covalent bonds because of this electrostatic interaction, but there is a sliding scale between covalent and ionic bonds.

Now, when salt is dissolved in water, something interesting happens. Because water is polar (as described above), it also has electrostatic interactions with NaCl. Enough of the solvent water molecules are able to gather around the salt such that the combined electronegativity of water is enough to rip the sodium from the chloride ion. Na+ is surrounded by the oxygen (negative) end of water, and Cl- is surrounded by the hydrogen (positive) ends of water. In this sense, water is physically separating the salt atoms from each other.

Covalent molecules like sugar are also able to dissolve in water because of slightly different reasons. In glucose, C₆H₁₂O₆, for instance, there are multiple–OH end groups, of which oxygen is electronegative and thus the terminating hydrogen is slightly positive in polarity. When put into contact with water, these hydrogen form electrostatic interactions with the oxygen of water, known as hydrogen bonding. Enough interaction makes it possible for sugar to also dissolve in water. However, the sugar molecule itself is not physically dissociated by water. This type of bond is highly effective as well, as evidenced by the solubility of the two aforementioned compounds in water. Sodium chloride is soluble up to 6.14 mol/L (Molar) in water, while glucose is soluble until 5.04 M.

This is a great question. Let's go back to the definitions of physical and chemical separations. Physical separations are processes in which substances are separated from one another by taking advantage of differences in their physical properties. Common examples of physical separations are distillation, chromatography, filtration, decanting, and centrifuging. Chemical separations are those where one exploits the chemical differences in a compound, and often involve changing the chemical state (e.g. precipitation). A common example is separating calcium from a calcium chloride and sodium chloride solution by adding sodium carbonate. Calcium carbonate will crash out of solution and can be filtered out.

In your example of the dissolution of NaCl in water, Na and Cl have not been separated in the sense of what is intended in the terms "physical separation" or "chemical separation." Na+ and Cl- exist as counterions in solution, and if you add enough NaCl to the solution, it will no longer dissolve but still exist as NaCl(s) salt. I hope this helps.

This actually relies more on the definition of "physical." The idea is that in this case, physical means "mechanical," that is, you can't take a piece of salt and pull it apart into two ions. Water is considered a chemical here, and it separates the compound by a chemical means. Here's a good video showing how dissolving NaCl is actually a chemical means of separation:

You're absolutely right that when you dissolve NaCl in water the compound does separate into ions. When I was in eighth grade (or so) I was taught to call any process that changes molecular structure a "chemical process" and any process that doesn't a "physical process." So, by that definition I would call dissolving a solid into a liquid a chemical process. Science textbooks sometimes say that it's impossible to separate a compound by "physical" means, but that's not a deep fact about nature it's just a rephrasing of our definitions.

Chemical compounds can be separated by physical means; otherwise polymers like hair, nylon, etc could not break. Similarly, covalently-bonded crystals (such as quartz or diamond) could not shatter. It takes a lot more force to break a covalent bond than an ionic bond or a Van der Wall bond, though, which is why minerals like quartz and especially diamond are so hard.

However in the case of NaCl, the bond between the sodium and the chloride ions is entirely ionic, meaning that the attraction between them is purely the electrostatic attraction of the positively-charged sodium to the negatively-charged chloride. In water, the sodium ions become attracted to the negatively-charged oxygen end of the water molecule, and the chloride to the positively-charged hydrogen side, which allows the two ions to become separated, hence dissolve.

You are correct that a compound can't be separated by a physical change. However, when you put NaCl in water, although the water looks innocent, it actually reacts with the NaCl and a chemical change takes place.

The water molecules interact with the sodium and chloride ions and break them apart. Instead of having strong interactions between postively charged sodium ions and negatively charged chloride ions, water separates the charges and creates new interactions between water molecules and individual ions.

You can think of it like breaking bonds (ion-ion) and making new ones (ion-water), so it's not a physical change.