abid,
The circuit that is shown in 4.png represents a circuit of a diode and the package parasitics, and maybe a bit more.
The basic diode (and transistor) models in SPICE are good for on-chip semiconductors but incomplete for separately packaged components which typically have lead inductance and capacitance of the attachments.? When someone needs the added detail of package parasitics, they can add them separately.? In 4.png, that includes Cp, Ls, and probably Rs.? Capacitor Cj might be part of that too, but Cj(V) depends on voltage so it is more than just that.? The built-in diode model in SPICE already has a junction capacitance Cj(V) that depends on voltage, so adding another one is normally not needed.? On the other hand, if the SPICE diode's Cj(V) can not be adjusted to fit the actual diode's Cj(V) with enough accuracy, then they might add the separate capacitor shown in 4.png.
It is difficult to answer your questions about Cj(V).? As I say, SPICE's built-in diode model already has a Cj(V) that depends on voltage in the way that most diodes do.? But sometimes people want to "take control" and do it their own way, instead of using the built-in SPICE models.? I do not know if step-recovery diodes have different capacitance Cj(V) than "other" diodes.? Since SRDs are used in extremely high frequency circuits, it's probably important to get that characteristic just right.
This probably does not entirely answer your question, especially how it relates to equation 2 in one of the papers.
Andy