The leak around the stem can be fixed by lubricating the stem and tightening up the stem packing nut.
The vibrating noise is probably a loose or damaged bibb washer on the stem, also easily fixed.
For what it's worth ( 2 cents!) bibbs should not normally be left on when not in use for any long period ( over 10 or 15 minutes.). The stem packing is not that rigoruous, and the hose itself also is not designed for that.