1997 Mitsubishi Eclipse Strange Noise

I own a 1997 Mits Eclipse with about 113000 miles on it and since I bought it last November Ive had a few problems with it. I have two major problems that I'm mainly concerned about and hopefully you can help. 1) When I drive (especially when cold outside) I hear a weird humming noise as if my car is a go-kart or something when I drive, the noise isnt only when I drive though, when I turn the wheel hard right or left in park it makes the noise but at a lower level. I've spoke with many friend mechanics who are puzzled by my description.
2) I have a grayish white smoke, not that thick coming from my exhaust. My main concern is that it would be a blown headgasket because I had to replace the head cover gasket when I purchased the car, but a friend mechanic said if it was a headgasket it would be a thick white smoke. I am really in need of help because I would hate to be driving my car right now if im making the problem a lot worse by doing so.