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Through which medium is most of the heat transferred down (downwards) a glass tube filled with water: the glass walls or the water column?

Whether glass or water "wins" depends on both the thickness of the glass (as Jim Clark correctly described) and the Rayleigh number of the water in the column. Wikipedia does a good job of ...
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Heat transfer: does the heat generated in a cable get transferred to the electrical components?

Most of the heat generated by the cable will be emitted by conduction, radiation and convection to the surroundings like the cable tray and the air. A tiny bit may get conducted to the board but that ...
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