In The Hobbit, in the "Queer Lodgings" chapter, Beorn explains to the company the dangers that they might face through Mirkwood:
“But your way through Mirkwood is dark, dangerous and difficult,” he said...
And the dwarves seem like they had no idea about it, or at least they didn't seem to consider crossing Mirkwood that dangerous:
But their spirits sank at his grave words, and they all felt that the adventure was far more dangerous than they had thought
Wasn't Mirkwood in this dark and dangerous state when the dwarves were still in Erebor and when they fled Erebor, since Sauron was in Dol Guldur during that time? Is the more detailed history of Mirkwood something that Tolkien only considered afterwards (when writing The Lord of the Rings)? (I guess a possible explanation is that Mirkwood was in a slightly better state when they left Erebor, since Sauron was gradually getting stronger.)
Is there any information available regarding how the Dwarves fled south from Erebor and arrived in Dunland? (e.g. if they crossed Mirkwood via the Old Forest Road etc) Because the company's original plan was to cross via the Old Forest Road:
By his advice they were no longer making for the main forest-road to the south of his land
Was the Old Forest Road known to be "open" when the Dwarves fled Erebor? Wouldn't at least Gandalf, who had visited Mirkwood more recently be aware of the state of the road (and Mirkwood), which according to Beorn:
Beorn had warned them that that way was now often used by the goblins, while the forest-road itself, he had heard, was overgrown and disused at the eastern end and led to impassable marshes where the paths had long been lost