Overnight is the standard overnight wilderness permit. Overnight exiting Mt Whitney means you are going in on a trail other than the Main Mt Whitney trail, and you plan to exit on the Main Mt Whitney Trail. There is a separate and second permit required if you want to exit to Whitney Portal using the trail down from Trail Crest. The thinking is that the trail is so impacted, and that many people were hiking to Mt Whitney from the north and south, that they need to limit the number of people hiking down the trail. So if you select the "...exiting..." part, it is way harder to get the permit--they won't let you get the entry permit if the exit permit quota is already full.
"...some marked W..."
Except for the Main Mt Whitney trail lottery (both day use and overnight), all other permits are 60% reservable (6 months in advance), and 40% held back for walk-in (the day before entry). It used to be they came available at 11 AM on that day before, but not sure now. The W represents the held back walk-in permits.
Not sure about the "Thursday" question.
"Next 5 Days" button: It works for me, but I'm using a browser on a full-screen. I tried it on my iPhone, and it shows "next 4 days", and that works ok, too. Maybe try a different browser.
