You won't get away with H+ in either case
It's incorrect to refer to the acids as "reagents" since they're catalysts. "Reagents" may have the connotation of the chemical species being consumed in the reaction eg acidified dichromate aka Jone's reagent in alcohol oxidation reactions.
For alkene hydration VCAA actually accepts any inorganic strong acid except for HCl (because HCl adds onto the double bond). States aren't required for the catalyst for alkene hydration. However you should still specify H2O(g) with states
VCAA only accepts concentrated H2SO4(l) for esterification, they don't accept anything else (which is overly pedantic since in uni chem we do all our esterification labs with a H3PO4 catalyst)