For circuit (1), the bias arrangement for a solid-state photodiode must bias anode at a more negative potential than cathode...so that no-light results in no-current (or perhaps just leakage current). It is also acceptable to bias with zero volts.
With infinite load resistor, no diode external current flows. Any internal diode capacitance simply charges up to some DC voltage. Response time is slow. A low-resistance load resistor speeds response time immensely.
This circuit (1) is DC-coupled, so it is not clear if photocurrent response is required to extend to DC:
For very large RL (similar to internal diode resistance) output voltage is not a linear function of incident light level especially at high exposure.
For small RL, voltage across RL is close to a linear function of incident light.
Circuit (2) appears designed for high-speed response. The internal bias resistor, and coaxial output (coupled with a series capacitor having no lead inductance) is designed to drive a 50-ohm load. Such an AC-coupled output is certainly meant for fast response time.
With this circuit, one might be cautioned to apply a high bias voltage +Va slowly, so that turn-on transient does not couple a huge spike to the external 50 ohm load RL. Such a transient could destroy a sensitive amplifier. Connecting a 50-ohm load after applying DC bias +Va could similarly discharge the internal 0.01uf capacitor as a huge transient into a 50 ohm RL. An internal large-value bleed resistor would be a good idea if +Va is large...this should be inside the shell, with the shell permanently grounded.
simulate this circuit – Schematic created using CircuitLab
Yes, the dynode voltage divider ideally is a simple voltage divider in circuit (3). Resistors are chosen large enough not to load down the high-voltage supply excessively, yet small enough that dynode photo-currents are a small fraction of DC resistor current. I recall something like 100k resistors in the dynode string. These photomultipliers are mostly used at very low light levels (yielding small photocurrents), but be aware that dynode currents are subject to gain.
The load resistor attached to anode is a small fraction of dynode resistors. Just like circuit (2) a permanent load resistor might be a good idea to discharge any DC anode voltage to ground. For example, a 1k resistor wired directly from anode-to-ground might help prevent a charged-up coax from destroying a 50-ohm preamp with a single-pulse turn-on transient. I'll bet more than a few preamps have been destroyed this way.
A more casual approach might caution a user, "Increase DC bias slowly to its final 1000V".