Do they still have oil rigs as lego sets? It seems like something that'd be a bit odd today, given the charged nature of 'oil' in world events and public perception...but maybe I just read too much internet.
There hasn't been any oil rig set since then, although one or two sets had oil rig models as alternates. However, there has been a gasoline related set of some sort every year or two.
You definitely need to stop reading so much internet.

Am I seeing this right that the Lego dudes didn't have arms and faces back then ?
I mean I remember the solid translucent blocks that were used as windows before the clear window parts were introduced, but Lego men without faces are just haunting.
Yes, the standard minifig came out in 1977. Before that they had no guys at first, followed by these faceless ones for a few years.