Detachments, how big do they need to be??

It is a tricky question. From a standpoint of requirement: there isn't one, a single battalion could technically be a detachment. From a standpoint of practicality, it is a job-specific judgement.

Commonly the intent of a detachment was to do as you say: Cause the enemy to deploy early and slow them by making them fight earlier than they wished. When it comes to this strategy, the player needs to consider 1) how long are they looking to delay the enemy and 2) how do they themselves intend to spend that time – i.e. what are they gaining?

One reason to use detachments is to attempt to do different things at once, you need troops in multiple places to cover multiple fronts, etc… It is often not a choice situation as you may likely be making a gambler's decision between being larger, thus with more staying power, but being hit from multiple vectors at once; or being smaller, thus will less staying power, but being able to confront each threat.

Big formations appear to have a big bonus over smaller formations, why create brittle smaller formations and weaken the larger host formations?

Detachments work best at natural choke points where enemy deployment will be slow due to the terrain, in this way they can be used to bottle up the enemy. Similarly, in opportune locations along a defile is also a good place for harassing detachments. The Prussians combine these at the Katzbach in 1813; the French are sending ployed Formations up onto a plateau via a narrow defile and the Prussians place mixed arms detachments with schützen companies in villages along the way to slow the French and beat them up a bit so that few fresh troops reach the plateau. Alternatively, the French can choose to deploy and flush each village, but that means their advance halts at each village to fight…

Funny enough, many players have made the observation they feel smaller Formations are more favored in ESR! The reality is that both have some ups and downs, but local superiority always has a net benefit.

Playing ESR, I did get the feeling that I was commander of large body of troops, I especially liked how I couldn't stop my lead Austrian division from plowing on in the attack

Excellent!

we both got the impression that some battles with only a couple of formations a side can be over very quickly

Obviously it depends on the strategy of the players – and the dice have a notable impact – but you are not wrong. Small engagements in ESR can be played very quickly. Mir in 1812 from Master of the World there are only a handful of Formations per side, and all cavalry. The scenario – if played as staged – can be over in as little as 15 minutes. It also plays on a very small table: 2 miles square. These scenarios can make for good jump off points for new players. Play them as historically staged first, then reset, but alter the setup to give yourselves some more freedom of decisions and go from there. Because they play so quickly, you can actually play a handful of variations in an evening and it can be a terrific way to get sequentially get a better understanding of the game.

I also liked how the terrain really impacted the battle. When the Bavarian detachment (broke) and cavalry division retreated, they both had to run along the north bank of the Danube. They where right next to the Bavarian infantry division when it was pincer-ed by the attacking Austrians. This played a big factor on the Bavarian assessment test, causing it to retreat after 1 turn of combat.

Sounds like between that and the combat die rolls the Bavarians need to change out their luck/dice, it appears nearly everything that could have gone against them did!

One factor to strongly keep in mind is that the Bavarians are largely playing this scenario with two practical goals: Do as much damage to the Austrians as possible while not allowing all their Formations to Break [BK], and second: last until the Saxons arrive. If successful, the Austrians will balk at having to confront freshly arrived troops. It isn't an easy task though obviously. An important choice is if the Bavarian player is going to try and keep the Austrians off the field. Since the Austrians are arriving somewhat dispersed, detachments – and the cavalry – are sometimes best used offensively to stymie arrival and connection of the different enemy elements.