I'll answer these backwards. When we train, we use a variety of grips. Close, med, wide, extrawide, etc...and rotate them during work sets. When we make max effort attempts, unless it's grip specific move (like close grip 5 board) or something like that, we use the grip we can move the most weight with.
Leg drive is hard to explain, even harder to show, but once you feel it, you know it. I think of it like a crowbar, although I think that analogy only makes sense to ME. I use my legs to SMOOSH my upper back (which is pinched together tightly on the bench through the entire movement) into the bench. Then the "return force" is UP/OUT. Like with a crow bar...you push down on one end, but because of the curves and angles in the crow bar, the force goes up. One way to realize your leg drive is to do floor presses with your legs straight out in front of you. You may catch yourself wanting to use your heels, or bring your legs in to get the weight up...it's because the legs DO play a big part in the force behind a strong bench. It's a full body press.
Most of the guys I see keep there legs out and wide when benching. Getting stable footing, and driving into your upper back will help you keep your core tight, and might help alleviate some of that lower back strain you are feeling. Keeping the traps (which extend down to the middle of your back between your shoulder blades) tight will also help stabilize the head and neck.
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