The Ecell shows that Zn is enough. Then why, are both of them required? Also, can I use any acid ? Or only HCl + H2SO4
A big factor is kinetics. A lump of zinc or even zinc powder sits there undissolved in a neutral solution and does not provide good contact with the chromium species with which you want the zinc to react. Adding acid creates nascent hydrogen in the solution, and this is what really does the job of reducing the chromium species. This source, drawn from a related answer by Nilay Ghosh, explores the matter more fully, and I recommend going there. In addition to the nascent hydrogen, the acid enables keeping the zinc ions in solution as a salt, where otherwise they would form a hydroxide precipitate that interferes with the reaction.
Not every acid is equally good. To get the most nascent hydrogen you need a strong acid and, even more important, one that does not eat up its hydrogen with other oxidizing functions (nitric acid, you're out!). Add the fact that cheap is also good, and hydrochloric and sulfuric acids are the usual choices.