1. Could Druids wear non-metallic armor? If they did, what happened?
Of course they could! Their choices were leather & wooden shields. If they did their AC improved.
The questions that we
did have to answer concerning Druids & armor were for studded leather & padded. Especially padded.
We eventually decided upon yes to both of those. Though for padded armor it's only ever been a point of discussion as I've
never seen a PC - of any sort - ever choose that option.
As for the metallic armors - chain, plate, etc? No. And the book told you why the class lacks that option. Pretty much the end of that discussion.
Except....
But what about for some RP purpose - like disguises?
Believe it or not, that type of question did come up. We ruled:
A) As per the description in the PHB it spoils with your magical powers - wich we decided meant virtually every class ability, not just your spell casting.
B) The best AC you'd get would be = to studded leather,
maybe, & determined by the DM on a situational basis. And any magic properties wouldn't function. Yeah, you're wearing better armor. But you don't know how to use it effectively.
This
wasn't meant to encourage wearing forbidden armors, it was in case we needed to know an AC is some misc circumstance while you were disguised etc
C) Metallic shields simply wouldn't work at all for you AC wise.
2. Could Clerics wield edged weapons? If they did, what happened?
In general, NO.
Sometimes though we'd change this up depending upon the deity chosen/campaign reasons.
Trying to use a forbidden weapon would result in failure. And you couldn't use any magical properties.
3. Could Monks use flaming oil? If they did, what happened?
No. Though I don't remember what if anything happened. But monks have always been rarely used, then or now, in our 1e games.
I suspect that back then we did as we do today - we look at that restriction on the chart, shrug, & go "OK, because...reasons." (and then pick a different class

)
So, my answer to questions 1-3 is simple- no, they couldn't. There was no grand, epistemological debate ("what if a monk had to pretend to be an oil thrower"), this was just a feature of the class- asking these questions was the same as asking, "What if the Assassin wasn't evil," or "What if the Thief wants to wear plate?" or "What if Paladins weren't stupid and terrible?"
Because of that, there was no need to answer what happened if they did.
Yeah, that pretty much describes our approach.