Dichromate is the reagent, the acid added is the catalyst.
A catalyst is something which speeds up the rate of a reaction whilst itself having no impact on the physical state of the product. A reagent is something which as added to another substance to cause a physical change (or something along these lines).
In order to hydrate ethene to convert it into ethane, you have to add water (obviously), which is the reacting agent - it causes the reaction. So that the reaction doesn't take forever, you add H3PO4.
Conversion of a primary alcohol to a carboxylic acid is called oxidation. So you need an oxidant, and dichromate happens to be a very good one. Once again, it is a reacting agent. We add H+ ions as well so that the reaction between oxidant and reductant happens sooner rather than later.
In esterification we have two reactants, an alcohol and an acid. This is enough to form our final product, so we don't need any more reagents. However without a catalyst the reaction would take thousands of years to happen, so we need to add sulfuric acid in liquid form. EDIT: So in a way, the catalyst is here a reagent, but it's not consumed in the reaction like H2O was in hydration, and it doesn't change form like dichromate does in redox.