Q:

Was the speed of the attack at Jena critical to victory?

[i narrowed the focus of my original post]
Many sources explain that the Prussian army was not anticipating the entire French force in the battle of Jena during the Napoleonic Wars. My question is whether Napoleon's speed in attacking had any effect in causing this. Were the Prussians not expecting Napoleon to get there so fast?

A:

The speed of the attack was absolutely critical. The French initiating an attack took the Prussian forces by surprise, forced them to split, and prevented their Russian allies from aiding them.
In early October 1806 the Prussian-Saxon army, under Charles William Ferdinand, moved slowly westward through Saxony in an attempt to threaten Napoleon’s communications to the west.  Napoleon advanced his forces northward rapidly to cut the Prussians off from the Elbe River and engage them before their Russian allies could join them.
The French victory at Jena, and subsequently at Auerstädt, effectively dissipated the Prussian forces. This victory allowed Napoleon to complete his conquest of Prussia within six weeks, before Russia could act to aid its ally.

Sources and suggested reading: 
Rickard, J (16 August 2012), Battle of Jena, 14 October 1806

