Peak Oil is a theory based upon assumptions.
False. The theory does not rest on any assumptions about future demand. Regardless of whether demand skyrockets or plummets, the rate of production is destined to decline at some point. It is not a matter of if, but when.
That is another assumption right there.
I would argue that oil is not finite. Oil is merely organic material that has changed to that state. Oil can be grown from plants, as it of course is also organic material. So long as people are able to grow plants, we can continue to produce oil.
I consider oil as renewable a resource as solar, wind or hydro. It is essentially a conversion of solar. It doesn't have to eat up all the farmland or fresh water either.