Western writing systems - the Italic, Greek, and Cyrilic alphabets - are written left to right. It is usually supposed that this has a practical reason - when writing with ink, the right hand moves to the right without touching the still fresh ink of the recently written words. And most humans are right-handed, for reasons I ignore (and I suppose science ignores too, albeit this pseudo-scientific evil conspiracy called evolutionary psychology probably having its two cents of illogical and unfalsifiable pseudotheories about the issue).
But Arabic alphabet is written right to left, and it doesn't seem its users actually have a problem with messing the ink with their right hands. So it might be merely contingent; if you flip a coin, it will give you either head or tails, and there is no use to speculate on the "reasons" why it ended with tails up ex post facto.
Two of the issues you point - the order of years in timelines and the order of books in shelves - are directly related to the way we write. I do not know if timelines or shelves are organised differently in countries that use the Arabic alphabet, but it would be logical, and I suppose that if it is not the case, it is probably due to Western influence.
As for the order of the keys in a piano - and other keyboard musical instruments - it seems to follow from the fact that our musical tradition puts more emphasys in the higher voices(1). We hear the soprano, the violin, the flute conducting the main melody, while the baritone, the cello, or the bassoon, play a secondary role, providing harmonic support for the main voice. In a keyboard instrument, consequently, we are to expect that the higher notes will be melodic and involve more complicated hand movements, while the lower notes will provide harmonic support. As most pianists, organists, etc., are right-handed, it makes sence to put the lower note keys to the left.
(1) "Higher", here, in a merely acustic context, as in, "higher wave frequency", not implying any superiority.