Sergey--
Get some of these anchors from home depot. Mark where you want the anchor, and just use a cordless screwstik to drive the white anchor in flush with the wall, then follow with the screw in the middle. They are rated at 30 lbs.
As for hanging stuff on the door, the centers are generally hollow core. If you try mounting more towards the top of the door, the first 4" or so should be solid.