power steering pump help, searched

Alright guys, started about a week ago, but when I turn my car on, Im pretty sure its the power steering pump just makes a constant noise, its realll loud, ive stuck my head in there and it sounds like its coming from the power steering pump. My steering has not been affected at all, when i turn the wheel it dosent get louder or quieter, when the engine spins faster, it does not get faster, it stays constant, but its not a whine, its kind of a deep hmmmmmmm, it does get louder sometimes but by itself, it sounds like its about to blow up. After like a mile or 2 of driving it goes away. Sometimes it dosent even do it now when I turn my car on. But usually when its cold it'll do it. Is that a symptom of a bad pump?

Few more questions, I work at a parts store so I've taken a look at a pump for my car, but the thing is just covered in this purple fluid, inside the box, the whole pump, all the extra bolts, idk, I mean is that normal? For some reason it seemed like there was fluid already in it.

Also how do you go about taking off the pressure hose?