yes the first problem is most likely Axle not power steering. my friend has a Hatch Without PS and It doesn't Shake/Rock Violently like you describe. if it doesn't shake like that going on a straight line then its most likely your axle like Joshuase said. Its giving you a sign that its bout to break/Pop. You should take a look at it by Turning your wheel all the way and looking at the boot. if its torn and grease is leaking out change that one. If you can't find one thats broken/ try shaking the axle. its supposed to be stable so if it moves its not good.

2nd problem cant really tell by words. probably need to listen to it. and i thought the redline for DA b18 was 7k? but yeah if its detonation try using premium. i really dont know what to say on this one. hope you figure it all out.