Yes, that makes a difference. You need a proper HPS ballast for your bulb to work. You'd be better off buying a 150+ watt HPS (with ballast) rather than bothering with that 70. You'd struggle to grow one plant with only that thing.
Probably not, the only lights I've seen at home depot or lowes are low wattage outdoor lights, not very good for growing. You'd pretty much have to order online or from a proper grow store.
