When referring to Oil "Erdöl", is the term "Abbau" correct, or is it just for coal and other minerals?
No, it is only used for mining raw materials in solid state and wouldn't work for liquids or gases.
Abbau literally translates to deconstruct, to take apart. It is the opposite of aufbauen, even when used metaphorically (aufbauen: build up, improve; abbauen: reduce, degrade). Both meanings don't really fit in the context of extracting liquids from the ground.
As Emanuel already stated, the most common terms are Förderung and Gewinnung.