Why was Omaha beach so dangerous for invading soldiers, especially in relation to the other beaches?
Why was Caen so difficult to reach and take?
What enabled the Allies to finally advance with speed in France? Was it simply getting out of the bocage?
Omaha - I highly recommend John McManus' new book, * The Dead and Those About to Die: D-Day: The Big Red One at Omaha Beach. It covers the problems really well.
The first is the beach itself was a poor choice. The shingle was mess to land on. And the whole beach was backed up by a large sea wall. The other beaches (except Utah) were similar but the wall was highest at Omaha.
The second is the landings had problems. The whole day, there was a strong cross tide. Because of this virtually no units landed where they were supposed to.
Third, the defenders were much stronger than anticipated. The German 352 division was supposed to be around 20 miles inland. Instead the Germans had moved them up starting in March, so that they were right on the beach.
Fourth, the preparatory bombings were ineffective. The night bombings had missed the shore and had bombed targets inland. And the naval bombardment was ineffective. It was only well into the morning that the navy started properly targeting German positions.
So on the German side you had more troops than expected and they were well protected in good positions. The Americans on the other hand were landing in the wrong places, and frequently had to fight their way back to where they were supposed to have landed in the first place. This especially wrecked havoc on their vehicles, specialized units, officers, and non-coms all of which seemed to take disproportionate losses.
Caen - Caen was a terrible fight, mainly because that is where the Germans decided to fight. The area around Caen was recognized as being better for the attacker (flatter, less bocage). And so the bulk of German reinforcements (even before D-day was done) went there. The Allies didn't achieve any of their D-day objectives. So it isn't surprising that they didn't get Caen either. And once the Germans had reinforcements in, it was a tough nut to crack.
The idea that this was Montgomery's plan all along seems to be a post hoc justification. But in any case it worked. The British pinned the bulk of the German forces in Caen while the Americans cleared the Cotentin peninsula and Cherbourg.
The Breakout - The breakout happened for several reasons. And the bocage was definitely part of it. Once they had fought free of the bocage, American armor could be used to full advantage. And even the infantry was in a much better position and not nearly as restricted to highly defendable roads.
The other parts were, the Americans had cleared the Cotentin peninsula and could focus all their attention to the south. Cherbourg had been captured and so opened a deep water harbor. It wouldn't be fully functional until September, but it started easing supply problems immediately. And the Allies had built up a local superiority in troops. So when Operation Cobra started it was 11 divisions against 8 (at least half of which were no more than half strength). And the US had total control of the air, and a greater than 10-1 advantage in tanks and self propelled guns.
Once the Americans started moving, the Germans didn't have good secondary defensive lines to fall back to. And all the reserves were committed to Caen. When they attempted to use them the British advanced and both sides of the front collapsed.
It is a great example of why the British and Americans adopted the tactics they generally used throughout the war. Build up forces until you have enough men and supplies to overwhelm the enemy. These broad front advances don't leave any significant weak points, and when the enemy collapses, it tends to cause the entire front to collapse at once, like a dam breaking.
The whole Normandy campaign is fascinating and of course has been covered extensively.
The Longest Day by Cornelius Ryan is probably the classic work on the landings
Caen: Anvil of Victory by Alexander McKee is a classic that covers the campaign from a largely British point of view.
and Six Armies in Normandy by John Keegan covers the entire campaign fantastically. And Keegan is such a great writer anyway, it's hard not to recommend him just on the writing alone.