#1 : From what I know (less than some, more than others) you can leave around 10:00 or so, planning on entering the Whitney Zone around 12:00. Take your time. Yes, permits "may" get checked.
It depends on the interpretation of what is the "trailhead." People are not supposed to enter any trailhead before midnight on the day of the permit. Since the main Mount Whitney Trail starts at Whitney Portal and the day hike permits used to be issued for the main Mount Whitney Trail, the original argument was that you should not be on the trail before midnight. Now that day hike permits are issued for the Whitney Zone, an argument can be made that the trailhead is wherever the route (MMWT or NF) enters the Whitney Zone. Lone Pine Lake is still in the John Muir Wilderness, and you cannot camp "overnight" without an overnight permit. You also cannot sleep on the trail with a day hike permit.
