When referring to Oil "Erdöl", is the term "Abbau" correct, or is it just for coal and other minerals?
It's "Förderung" or "Gewinnung".
"Abbau" doesn't fit, because you just have channel the oil, or pump it out. There is no "hacking" involved. Also, "Abbau" in context of oil means to "degrade" it.
"Förderung" is also used for coal and other minerals like gold, by the way.
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.