I drive a 2002 F-250 diesel, and whenever I turn the wheel and accelerate, especially at a low speed, it makes a low whining noise that gets higher as my speed increases. I checked my power steering, and it's almost empty. I'm going to refill that ASAP, but I'm wondering if that noise could be cause by anything else.

Also, this may be unrelated, but when I press down on the brake really hard, it makes a really rough noise and I can feel it vibrate in my foot. It does this when I'm not moving also.

Thanks for any help, I just got the truck used a week ago, so I'm not very comfortable with how she's supposed to feel driving just yet

 

Some of those vehicles had what was called a "Hydroboost" brake system. It uses pressure from the power steering pump to provide brake assist. Once you fill the pwr strg reservoir the problem may disappear.
Good move to determine where the fluid went though.