3. A fan with a given output will completely change the air in a small compartment much more quickly than in a large one, especially one with lots of nooks and crannies.
However, a large compartment will take longer to heat up. Independent of the compartment size, every second the circuitry is dumping a fixed amount of heat into the case air, and the fan is expelling a fixed quantity of air. When the compartment temperature rises such that the excess heat in that quantity of air equals the heat dumped from the circuitry, equalibrium is established. This equalibrium temperature is independent of compartment size.
If we look more carefully, it can still make a difference. Small compartment size means you'll have higher air velocity within the case. This means:
+ better flow over passively cooled components, which could otherwise form local 'hot spots'
- more prone to reducing the air-throughput due to obstructions.
(- more noise from airflow through the case, but this should be trivial.)
Unless you're making the compartment very crowded, or using passive heatsinks on important components, I suspect the compartment size doesn't matter much.