All digital ICs should have decoupling caps between their power and ground pins. These should be ceramic and physically as close as possible to the IC. You want to minimize the loop length from power pin to cap to ground pin thru the IC and back to the power pin.
Decoupling caps deal with short term current spikes the IC draws. They must therefore be high frequency. Large capacitance is not necessary, and since large capacitors usually have poor high frequency response, they are worse. A 100µF electrolytic cap is pretty useless for decoupling. 1µF to 100nF ceramic is good.
As for the cap on the motor, the idea is good but I think 100nF is too large. That could cause excessive or unnecessary current to flow in the H bridge every time it switches. If you're only reversing motor direction occasionally, then this isn't a big deal. If you're using the H bridge to modulate the apparent motor drive with PWM, then you should lower the cap. Something like 1nF should still cut down the noise the motor is making while not getting in the way of switching.
I only looked at one of your proposed parts, the Murata LLL153C80G105ME21. I compared it with a same-value part in a larger package (GRM21BR71E105KA99#, 0805 size), the key improvement is in the available voltage rating. The 0204 part is rated for 4 V, while the 0805 part is rated for 25 V.
Even if your application only applies 4 V to the cap, take note of the capacitance change with applied voltage charts. The value of the 0204 part will be reduced to a bit above 30% of nominal (e.g. 0.3 uF instead of 1 uF) with 4 V applied. The 0805 part will still be at 95% of its nominal value with 4 V applied, and only loses about 45% of its value at 25 V applied.
So the smaller part can be used if you can accept its reduced temperature range, but its value will be reduced to just a bit more than the 0.1 uF value that has been typically recommended for use as the near-chip bypass capacitor over the past decade or so. If you really want 1.0 uF of bypassing, you'll still have add some larger parts in parallel with the suggested 0204 part.
On the other hand, if you can live with the low WV rating and you use this part in place of the "traditional" 0.1 uF 0402 part (in parallel with additional larger-value caps), you will gain a 3 - 4x increase in effective capacitance, so that is a substantial improvement.
Also, in a high-reliability application, you may want to use a package at least one size up from the minimum needed for the capacitor value and WV you are using. The smallest available size is pushing the limits of what the manufacturers can do, and can have reliability issues.
Best Answer
Omitting the supply rails and decoupling capacitors is a common shorthand in circuit diagrams. It's admissible, when supply rails are not important for the discussion.
0.001 μF in the original post is not a decoupling capacitor. It's a compensation capacitor between pins 1 and 8 of the CA3130 OpAmp.
fig.8 on p.9 in the datasheet. Decoupling capacitors in this schematic are 0.01 μF, compensation capacitor in this schematic is 56 pF.