What is the natural replenishment rate of oil? Are extinction events connected with higher production?
Almost nil on human time scales.
The total estimated reserves (this number keeps changing over time) are of the order of 300E9 m^3. For convenience lets say all of this oil formed over the last 300 million years at a constant rate. Then the rate of formation is 1000 m^3 per year or ~6000 barrels of usable oil.
This obviously is a simple back of the envelope calculation and doesn't account for oil that has been lost/degraded/converted to other hydrocarbons over time. Also the rate of formation varies a lot (depends on climate, position/structure of plates and what not).