I've only read the first page of the thread, but IMO it is up to the DM. It does state somewhere that a creature with equipment in its stat block is proficient with that equipment.
I don't think it's necessarily true that an orc is proficient with a dagger just because it can use a greataxe. The orc is likely proficient, since daggers are simple weapons, but maybe this orc tribe considers daggers un-warrior-ly and therefore these orcs aren't proficient. I think that's fine.
As to the ape using equipment, that would be up to the DM. Of course, if I were the DM I would give a hard no, as that seems antithetical to the intent of BotE. The ape would be treated as non-proficient if it tried to use weapons or armor. I'd let it throw improvised weapons though, as that does seem reasonable for an ape to be able to do.