you can but will be wasting a lot of time/light. you should fashion one out of cardboard and emergency blanket until you get a hood. just make sure to keep it a safe distance from the bulb.
You can always try to hang your bulb vertically. It'll still be inefficient though unless you have a few plants to go around it. Never tried it but I've read about it and seems to work fine
You may be right. I think that's more with MH bulbs though. I thought most, if not all of the newer HPS bulbs were manufactured and designed for a universal mount. Either way, if it's something you're interested in just research your specific bulb and see if it would be okay to try. You get 360 degree coverage and you aren't wasting much light/lumens compared to having it mounted horizontally above the plants with no reflector. I've been thinking about giving this a shot myself. Look up some pics of people using this method, very impressive yields.