Equivalent circuit of a photodiode
What can I learn from an equivalent circuit model of photodiode


I believe you are overthinking this a little bit. While a model may not be of any use in let's say a technical datasheet, it can be pretty useful for designing circuits or perhaps research purposes. It also serves as a kind of mental image of a photodiode. People are usually graphically oriented, and models usually help to make sense of stuff.

Another important use for models, is to investigate how a photodiode would work in conjunction with other circuitry (eg. a transimpedance amplifier - TIA). We can use a model like this construct criteria and trade-offs that may prove necessary for the application. For example, the junction capacitance turns out to be very important for the stability of a TIA. From the model you can also see that \$R_s\$ could decrease the bias voltage, possibly increasing rise and fall times of the photocurrent. The photocurrent seems to be best modeled by an ideal current source, telling us that the bias voltage probably doesn't have much influence on the (DC) photocurrent. Etc.

Another use for a model is inside simulations. A Spice simulator usually doesn't include a model for photodiodes, and as such we may need to model it ourselves similarly to the schematic in your question.


  And why is nearly everything parallel to each other?


It just turns out that that is the best way to model a photodiode. There is actually little choice involved. We just identified certain parasitic effects, and when modeling them it seems to be best represented by shunted components.