Glad to help on that NG question. I had always been curious about these divisions. The information available was so sketchy, and what little there was did seem to indicate that there were NG divisions on each flank of the Armee du Nord, but I could never find any OOB for them whereas I could find something for the NG units in the secondary theatres. I cannot recommend Regnault highly enough for a person really trying to untangle just how Napoleon stood up his army in the weeks that he had available. If you really don't want another tie, do hint for the copy of Regnault on Bookfinder.
Regarding your questions, here's my thoughts on them:
"It seems to me that there were several missed opportunities on both sides throughout the week." Oh yeah, but WAY more by the French. Napoleon was sorely missing his old staff, not just Berthier, but many of the old team didn't participate.
"Could Ney have taken the crossroads if he was placed in charge of the left wing one or two days earlier?" A couple of days would have made no difference in the fact that he had no staff yet was expected to run a group of corps. Also he had shown in the past that such a role really was not his expertise. There were many other better choices for the role.
"He might have been able to close up his corps and not have them strung out over several miles. Would he have been able to defeat the Anglo-Allied army in detail as they came west from Nevilles?" That his troops were strung out to the extent that they were had a lot to do with the bottlenecks across the Sambre. Napoleon could have had one of the corps cross at Thuin, but decided not to, presumably to ensure that such a corps did not get bogged down so far south had it hit serious resistance. His objective was to gain a central position as a concentrated mass, with the intention to drive the Prussians east and race to Brussels. The evidence would indicate that he did not think that Wellington could concentrate adequately to cover Brussels. The other factor contributing to corps not being closed up was the quality of orders transmitted by Soult, in contrast with those that Berthier normally issued.
"Which direction would the Prussians have retreated if D'Erlon's force was able to come up on the French left as Napoleon desired?" Napoleon actually expected d'Erlon to envelop the Prussian right. At one point in his counter marching d'Erlon did come up on the French left rear at Ligny - not at all where they were expected. This lead to a near panic in III Corps and the necessity to ensure that this was not a thrust by Wellington. Had d'Erlon actually come into play as envisaged by Napoleon, I think three conclusions can be suggested. First that Prussian losses would have been higher, second that the retreat would not have been as well conducted and could have become a rout, and third that the route to Wavre via Tilly would not have been open as d'Erlon would either be astride or threatening it. If so, the axis would probably have been through Gembloux. From Gembloux, the Prussians could easily move to Wavre, however if a French force such as d'Erlon moved north via Marbais on the 17th, the route from Gembloux to Wavre was a flank march and somewhat risky.
"Where would the next battle between Grouchy and the Prussian III and IV Corps have taken place, if at all?" That would depend in part on how effective d'Erlon's intervention had been. You assume that I and II Corps would be so heavily damaged as to be out of the picture. It is not likely that the Prussians would have kept their neck in the noose if d'Erlon had shown up. Blucher would have broken off the action, even if it meant abandoning a number of units and guns. At least one brigade of III Corps would have been rushed from the left to the right flank to threaten d'Erlon's advance and bog him down.
"Would Kleist's corps figure in that fighting?" I doubt it. First, Kleist was in Luxembourg. His function was in part to cover the approach route for the Russians. Moving from that location would remove the security for the Allied forces approaching the middle Rhine. Second, he was at least 4 days march from Liege. Third, Moving further west to join Blucher would unmask the line of communications. If Blucher was indeed mauled and Wellington unable to hold his position at Waterloo due to lack of Prussian support, then the two Allied armies could easily be driven north out of Belgium. Fourth, Kleist's corps was not well organized for field operations. Have a look at the link to Plotho provided by Steve and consider the quantity of artillery in his corps. Fifth, Prussia had another four corps assembling to the East (including the Rhenish landwehr). Once again the details are provided in Plotho. Sixth, army politics. Kliest was senior to Gneisenau. Kliest had also been in command of the Prussian army in the Netherlands until being replaced by Blucher for the campaign.
"If Wellington could not count on Prussian reinforcement, where would he have made his stand? Would he have retreated on Hal to Antwerp as David Hamilton-Williams claims, or would he have acted more offensively? He did outnumber the French at Waterloo." Many people have issues with DHH and I think you will find it better to use sources that are not discredited. That said, you are correct that the line of retreat was north not east. The route from Ostend was used for supply since the sea journey from the British channel ports to Ostend was short and sea transport was a bottleneck. Wellington had no intention of being bottled up in western Belgium. A prolonged campaign in which Belgium was lost would require that the remainder of the Kingdom of the Netherlands was defended as long as possible and that Hanover was covered. Have a look at the campaign of 1793 to see how the British lines of communication went back to Emden, for a number of reasons. Wellington's army was not well configured for offensive action, and he tended to take offensive action in one of two circumstances - local superiority or as a thrust to place the enemy off balance. His army was nowhere near as cohesive as what he had had in the Peninsula and many of the units were quite raw. There was great concern before Waterloo as to how sound the Netherlands divisions would be, and this would be at least as much of an issue if the greater part of Belgium was abandoned. I am not sure what sources you are using to determine that Wellington outnumbered Napoleon at Waterloo. I think most sources peg the count as about 67K to 72K men and 150 guns to 250. Even if you throw in the flank guard at Hal, it was not enough to make Wellington that superior. Regarding the direction of retreat that Wellington had envisaged if required, have a look through the archives here keying on Antwerp and Maastricht. I think you should find some very useful posts from Bruno Nackaerts.
It is worth considering what was coming up behind each army. There was probably 15k+ en route to Napoleon, and possibly about as many more men every two weeks or so ... so long as he kept winning. Meanwhile the NG was filling up and the frontier fortresses becoming better garrisoned. On the other side, Wellington could expect to lose a quantity of Belgians, but gain additional Dutch units in training, plus the Danish and Hanse contingents were en route. Additional units were coming from the UK and the US. On balance you can figure his numbers would stay pretty solid at 80-90K in a field army. The Prussians had Kliest plus another 80-100k forming behind Kliest, so you can figure they'd have at least 140K in being even if Blucher was crushed at Ligny. The first 100k+ Russians were already crossing the Rhine. The Austrians and south German contingents were ready to cross the Rhine. Even if driven north, I am sure that Wellington would have been quite content, with Blucher, to continue to hold Napoleon's attention while Barclay and Schwarzenburg moved on Paris. Napoleon was seeking to maul both Wellington and Blucher to such an extent that they would be unable to attack the north of France effectively. If he could do in a couple of weeks then hustle towards Metz he figured that the fortresses in the north would soak up the crippled armies of Wellington and Blucher. He then probably calculated that with a field army of 200,000 men (the Army of the North, V Corps, continued reinforcements from the depots and some National Guard) that he would be able to handle both Barclay and Schwarzenburg. Both Wellington and Gneisenau both probably could divine this intention and knew that their best shot was to unite to defeat Napoleon, and if they could not do so, to keep their armies in the best possible condition, ready to take the offensive the moment he turned his attention elsewhere - in effect repeating the strategy of 1813 leading up to Leipzig.
Keep thinking those deep thoughts - it's a fascinating campaign for "what-ifs". Regards,
David