Mike70, that's a really aggressive plan when it comes to the altitude. AMS could hit you if you go much above Trail Camp on the second day, but you might be lucky -- it just depends on how well your body adapts to the altitude.
Nobody can predict how long you will take for any section of the route. It depends on your condition and abilities. Just look at the elevation for each section, and consider that the higher you go, the slower you will go.
With such a quick trip, I'd plan on camping at Outpost both nights, and attempt the summit on the second day. If you are strong (and lucky with the altitude) you might make the summit. You will know, as you climb above Trail Camp how far you can go. Do not go above Trail Camp without crampons and ice axe!
Permits are good for anyone (no quota) through April 30 (Friday), and they are designated by the date you start the hike. If you start on an overnight trip in April, that permit enables you to stay as many nights as you want. The quota and permits starting May 1 or later only apply to hikes that start May 1 or later.
