Morkus from Orkus
Basic monsters would be orcs and goblins, maybe trolls and ogres. Anything more is rare and not basic. And that's if there's a fighter's guild and if you happen to be a member, rather than Joe the Farmer adventurer who picked up a sword and went out to seek his fortune.Everything? No, but most stuff -- absolutely! It would be a weird world where the guild of fighters doesn't have library containing multiple copies of "Basic Monsters and their Abilities". Even in our world, those kind of books were best seller in the medieval and ancient world for people who were just curious!
Not in D&D. You seem to be under the misapprehension that all of the monsters are roaming the world in packs or something and people are putting the info on some magical internet. The PCs encounter monsters at a rate that is incredibly higher than the world at large(including fighter's guilds). If it wasn't, then the world died to monster invasions millennia ago.If you were a specialist, you would not only know the MM, MM2, MM3 and every other book possible, but would have studied variants of all of them, misprints, notes on each of them by reknowned authorities -- a huge amount more.
There aren't enough high level people in the world, even in the Forgotten Realms, to handle all the monsters in the books if encountered at the rate that PCs encounter them. The PC's are special that way in order to make the game playable.
Decades of specialized study like a non-combat sage.Knowing the contents of the MM is pretty trivial. How long would it take you personally to memorize it well enough to pass a basic exam. Two weeks? A month?