Electronic – Different decoupling capacitors in parallel

Second question first -

• 2 x 680 uF often will have a better ripple current rating than a single larger cap - sometimes very significantly so.

• 2 x 680 uF also may be lower height or easier to fit in board space - MAY have more area but be less obstructive than a single larger cap.

• Also, as you say, ESR may be better, but often a single large cap is as good.

The 0.1 uF capacitor is intended to remove very high frequency components better than the larger capacitors do.

The small capacitor will usually have have low ESR, low lead and internal inductance, a higher self resonant frequency and a lower overall impedance at higher frequencies. At least, that's the plan. Reputable manufacturers may publish tables showing impedance with frequency and from these an excessively keen [tm] designer can provide a filtering combinatuon that produces a best overall result. It was tradional to consider a 0.1uF cap as the standard HF filter cap but there have been two schools of though to that in recent times.
One argument is that increasing frequencies of both smps and processors and target ICs make smaller caps better suited to the typical frequencies. The other holds that the new ceramic caps are far superior to those of eg adecade ago and that a 1uF or even a 10 uF ceramic will do a fine job at relevant frequencies. Both arguments have merit. If you use a 0.1 uF moderm ceramic instead of going to a 1 uF then you arguably get the benefit of both arguments :-). (ie it's bigger than you might have used and smaller than you might have used).

I do not see at a quick read anything that says where that capacitor is physically located. While the caps are shown sequentially on the diagram, that is only an electrical diagram and actual layout is not strongly suggested by it. General component placement will often have some reseblance to circuit diagram flow but nothing is necessarily fixed. In this case the 0.1uF can be phyically near the cathode of D1 and the ground side of R2 R14 R16 and that is where I would try to locate it.

Cypress excellent - Using decoupling caps

How to select bypass caps Goodish

Tends to suggest that bigger is better mostly :-) :
From this excellent guide - A practical guide to high speed PCBB layout

Useful and related but not 100% on topic here Useful

Related - caps and ESR Wikipedia

Regarding the capacitor, Ignacio beat me to it. shakefist You'll see capacitive coupling all over the place in circuits like these.

As far as what you feed in, actual amplification will depend on the resistor values. The specs say -.3 to vdd (your source voltage) + .3V, so provided your VDD is >= 3 volts, you should be able to amplify to that level.

update

You can simply leave the V01 disconnected. The speaker wire connected to pin 5 in that schematic would be connected to ground instead.

That said, the configuration shown in the schematic is said to have a gain of $$2(\frac{R_i}{R_f})$$ This is because the outputs are 180 degrees out of phase with eachother, so that even though both amplifiers being unity gain (when Ri = Rf), it winds up doubling the input.

If you don't use pin 5(V01), you'll need to adjust your gain. The new formula would be $$\frac{R_i}{R_f}$$

That said, if you haven't already ordered a different chip, I think the LM4880 is more in line with what you want, it's mentioned in the automatic switching circuit in the datasheet, and it's a single output headphone amplifier.