The power steering is a separate system to the engine. The power steering system consists of a pump, bolted to the engine. A steering box, bolted to the vehicals frame and two hoses carrying fluid back and forth between the two. There is no power steering hose "in" the engine.

You will screw your steering system. You need to flush steering system ASAP. And of course do not drive with engine oil in steering.

In the power steering box.

It is on the left side of the engine under the engine cover. It has a steering wheel on it.

It is the engine that is vibrating and it is just being felt in the steering wheel. Can be a vacuum leak, or miss in the engine.

The hydraulic seals in your power steering will be eaten away by engine oil.

Your power steering will start to leek and eventually, it will not work at all.