The above are good answers. To repeat: You only need a DAY hike pass for Mt Whitney. All other day hikes do not require permits.
Since you are starting at 10,000 elevation, (2k higher than Whitney Portal), you don't need to start at 1 AM.
You don't need ice axe or crampons.
Another alternate might be White Mountain. But it's another hour and a half driving north and east of Lone Pine, and the last 20 miles are on washboard-y sand/gravel road. It's even easier than Mt Langley, as it starts at 12,000'.
