LM35 bypass capacitors
so I would need a 0.01 uF electrolycal capacitor.

You will probably have a very hard time to find a 0.01 uF electrolytic capacitor. As 0.01 uF is only 10 nF I'd say that means it will be a ceramic capacitor.

In case 1 and 2 the 0.01 uF capacitor is optional, I would just add that 10 nF cap. Since this is a very low frequency application (nearly DC) it should not hurt to have the capacitor present.

If you're designing a PCB for this: just add (footprints for) the .01 uF cap. You can always later choose not to mount the capacitor.

The 1 uF in figure 13: you should add it, it is not optional. You do not have to use an electrolytic type, it can be ceramic or other non polarized type as well. Do add the 75 ohm resistor though.