First of all the explanations from The Stationmaster have omitted the concept of Starting signals. What's the difference between a home signal and a starting signal? Usually, a home signal is passed by a train before the signalbox; a starting signal is passed after the signalbox. There are exceptions, usually when the signalbox is beyond the end of a station platform.
You have labelled the signals wrongly in your latest diagram: a is not the section signal, but the starting signal; b is the advanced starting signal (which is the section signal) with the distant for the next signalbox and shunt-ahead signal below it; c is the starting signal (also the section signal) and distant, and d is the home signal. These would be distinguished by being preceded by "Up" and "Down", being the descriptions of the lines they reefer to. You don't have a home signal on the road through platform 2. You also do not show the position of the signalbox on your diagram.
Here's a question for The Stationmaster: Have you come across a distant backing signal? (Yes, at least one did exist.)