1. If the pipe was strong enough then only one thing can happen. The oil would go up the pipe. But I don't know if it would stop at a point or if the vacuum would be strong enough to suck it out the other end

on second thought if you took a tennis ball and put it in the pipe would it fly up to the top and out into space? Perhaps it would? In that case I don't see why little bits of oil wouldn't do the same. lol. I don't know enough about vacuums
2. If we could change the rotation of Earth that way it would have no effect on time. Only on our concept of time because we would alter the way we interact with the Sun. I'd like to think the molten rock nearer to the core would also spin the other way eventually like a big washing machine suddenly changing direction

haha. I suppose it would have some minute impact to strap all those rockets together

really don't know.
Also this whole thing with the speed of light and time...I dunno hey. I mean I often reason by taking something to an extreme to try understand what might happen as it gives a clearer picture. Say at point X in space where we are we notice something at point Y which is many light years away and we know by general knowledge that by the time it's light travels to us to observe it it is already so many hours/days past that point. Screw travelling faster than light. The extreme would be to appear there instantly at point Y right now with the snap of your fingers, what would you observe? Well of course the object at point Y would no longer be there obviously.
Simply because you observed it from point X so many hours later does not mean you can outrun it's light and catch it moments before the point of observation. I would say the state of matter as it is now is the same throughout the universe anywhere you look no matter how/when you observe it.