The rules state enemies get shadow cards at the beginning of the combat phase, so say, Smaug the Magnificent attacks again cos his shadow card had a burgle effect, does he get another shadow card for that attack? If so he could attack as many as four or more times in a row...

Also in burgle attempts when you 'reveal the top card of the player deck" does that get discarded or turned back down for drawing next turn?

Yep unless stated otherwise you deal a shadow card for all attacks including "additional" ones. Yeah that quest is notoriously difficult/broken for that reason. I've had him attack 7 or 8 times in a row or more on many occasions... 4 is nothing

Also in burgle attempts when you 'reveal the top card of the player deck" does that get discarded or turned back down for drawing next turn?

Reveal just mean look at for players card deck.

If so he could attack as many as four or more times in a row...

Or six or more...

I don't have The Hobbit saga expansions yet, so I'm not familiar with the quests beyond the glimpses of horror I've read in other players' posts… but I imagine that Song of Wisdom and A Burning Brand would be essential in this quest for at least negating the effects of Shadow cards dealt to Smaug?

Burning brand will not help you: Smaug's attack is triggered by the card having a burgle effect on it. Burning brand negates shadow effects which are different from the burgle effect. Your best hope is to use "Dawn Take You All" and remove the shadow card from play and bypass any chance of their being a burgle effect.

Ouch…