The essence of water absorption: all substances tend to be mixed as much as possible, which is called "entropy increase" in thermodynamics. That is to say, whenever the entropy increases (that is, the disorder and disorder degree of molecules increase), it can generally be carried out spontaneously, and the process of entropy reduction often requires human intervention. For example, if you dissolve salt in water, the process is very fast and you don't need other means, but if you want to separate salt from the solution, you need heating, blowing and other means. This example can show that substances are easy to mix, but difficult to separate. Because the more mixed, the more consistent with the initial state of material distribution in nature, the more stable. Similarly, pure sulfuric acid also has such a tendency to absorb water, because the absorbed water reduces its concentration, which is conducive to the stable existence of the solution. This is not because any particular particle has any special function, and phosphoric acid and sodium hydroxide solids will also absorb water, just a natural trend. In addition, high school should have said that exothermic reaction, whether it is a physical process such as reaction or dissolution, as long as it is exothermic, the product will be more stable than the initial state, so it can be spontaneous. I think this explanation is more acceptable to you.
The essence of dehydration: sulfuric acid removes hydrogen atoms and oxygen atoms in organic matter according to the composition ratio of water (2: 1), leaving only carbon atoms in organic matter molecules, that is, carbonization. In fact, it also comes from the strong oxidation of sulfuric acid.
As a catalyst: this involves the formation and stability of carbocation (we attribute the mechanism of these reactions to the production of carbocation intermediates). The higher the acidity, the easier it is to form and the more stable it is, which is beneficial to some reactions. In many cases, the acidity of sulfuric acid is not enough to make the reaction go smoothly, so it is necessary to use acids stronger than sulfuric acid, such as perchloric acid, fluorosulfonic acid, solid superacid, magic acid and so on. This part of the situation is a bit difficult for high school students, but if you are really interested, you will definitely learn it in the future.
Oxidation: Because the valence state of sulfur atom is too high, it is often easily reduced. However, in dilute sulfuric acid, only hydrogen ions play an oxidation role, and the oxidation ability is not strong, so copper can not be oxidized.
Esterification: The catalytic effect of sulfuric acid here is not because of water absorption, but because it provides hydrogen ions, which form samarium salt (an intermediate) with carboxyl groups in acetic acid, so that the carbon atoms of carboxyl groups become carbocations, which is beneficial to the approach of oxygen atoms (slightly negatively charged) in alcohol hydroxyl groups. After the combination of the two, the molecules are rearranged to form esters. In fact, this is an example of carbocation process. All strong acids can catalyze this reaction, but usually concentrated sulfuric acid is used as the catalyst for this reaction because it does not volatilize.
I hope my explanation can give you some preliminary answers.