It’s an ongoing process. When Tywin marches across the Riverlands, “they trotted past blackened fields and burned holdfasts, down to the Riverlands and the Green Fork of the Trident…Ser Gregor burnt out the Pipers and the Brackens,” and Tywin is already sending out “foraging parties.” That’s well before Tywin gives the order to burn the Riverlands from the “ from the Gods Eye to the Red Fork.” In the meantime, the Riverlords have been “burning their own crops to try and starve us,” as they did back in the Dance.
So no, marching on Harrenhal is not a miracle solution. If Robb wants to cut Tywin off from resupply from the Crownlands, he’s got to completely circumvallate the biggest castle in Westeros, which means stretching out his army to the point where Tywin could pull a Frederick the Great on him. Moreover, if Robb does this, the entire Riverlands – which he would be relying on for supply – is open to Ser Stafford Lannister.
Moreover, Robb’s supply situation is automatically worse than Tywin, because he’d be trying to support twice as many men as Tywin is.
Our first ebook, A Flight of Sorrows, was an anthology jam-packed with insightful analysis of the Song of Ice and Fire series, but it only barely scratched the surface of the huge and complex world that George R.R. Martin has created.
Assaults would have been extremely costly – castles offer extremely high defensive multipliers, and historically garrisons of a few hundred or even a few dozen men could easily hold off thousands of men. Moreover, while the combined force had a 2:1 advantage, the usual rule of thumb for battles in the open field is that the attacker usually should have a 3:1 advantage.
Heavy horse is unlikely to be an issue. Firstly, you can’t really use cavalry in assaults unless you dismount them. Secondly, Tywin is highly unlikely to have more heavy cavalry: he had approximately 7,500 horse at the Battle of Green Fork, and Robb alone had 6,000 horse at the Whispering Woods. Even after the Riverlands forces are dispersed following the Battle of the Camps, Edmure pulls together 3,000 horse at the Battle of the Fords. So Robb would have had at least 9,000 to Tywin’s 7,500.
The bigger issue would be supply – after Tywin’s initial rampage across the southern Riverlands, his reaving after the Green Fork, and the scorched earth tactics of the Riverlords, and camping his army for months on end, the area around the Godseye would have been stripped bare of food and other supplies.
If they’d attacked Casterly Rock, Tywin would have marched west same as in OTL. If you mean Edmure wouldn’t be around to stop him crossing the Red Fork, then Tywin is too far away to make it back to King’s Landing, the capitol falls, now Tywin’s a rebel, and Tywin would have been facing an army twice his own size out on open ground.
Yes there is. Given the emphasis on charity to the poor in traditional Christian teachings, nobility and royalty made a big show of helping the unfortunate – everything from giving leftovers and handmedowns to beggars at the gate to giving money to the church for hospitals and orphanages to giving alms on Maundy Thursday, to washing the feet of the poor in imitation of Christ.
These kind of gestures were a core part of the medieval social contract – the quid pro quo for deference and obedience was at least a symbolic expression of noblesse oblige.