Electronic – Two electrolytic filtering capacitors near or far away from each other

It depends a lot on your requirements as a simple logic circuit will run properly with just 100 nF and nothing else. If you have sensitive analog voltages the choke (or, maybe better, ferrite) can be helpful.

I don't think 1 nF and 10 nF will give you any advantage, but if you have a lot of input ripple or want very low output ripple, I'd add 10 µF on the right side (there are even ceramics in 0805 nowadays).

The inductor needs to be on the power supply side, not near the controller. If it would be there, the controller's supply voltage would drop seriously every time it switches something (internally or externally).

Multilayer ceramics are the new tantalum. ;) I guess, they recommend them in contrast to aluminium electrolytics because of their low ESR.

Your circuit won't draw much current, so maybe 100 µF electrolytic or less at the input? That's really just a guess because if you have a clean supply you probably don't need any capacitors at the input at all (but they won't hurt).

The most likely reason why that is done is because, in real life, capacitors do not have infinite bandwidth. Generally, the higher the capacitance of the capacitor, the less it will be able to react to high frequencies, while small-valued capacitors react better to higher frequencies, as seen in the graph below. Using two different-valued capacitors together is just done to improve the response of the filtering.