Yes, your permit allows you up to two weeks on the mountain.
The thing is, when you go and get your permit, they will ask you your exit date and where think you are going to camp each night. (Whatever you put down on recreation.gov, when you requested your permit, will be superseded, so don't worry about that.) You are allowed to deviate from what you tell the rangers, and people do all the time (and the rangers probably expect some deviation, particularly if conditions occur that make it safer to leave early or late), but keep in mind they are asking that information so that if something goes wrong they have a sense of where to find you.
If you think there is a likelihood you may stay 3 nights, it may be better to advise the rangers you plan to stay 3 nights (which you can do when you pick it up) and then exit a day early if you choose to do so. If you exit a day early, the rangers will be able to figure that out if they need to because your car will be gone (just as if, if you overstay, and the rangers need to know, they'll be able to figure that out because your car will still be in a lot).
If you choose to camp on the way down, Lone Pine Lake is prettier and quieter than Outpost camp (it is off the trail, while the trail literally goes through Outpost camp, with people on it at all hours of the night). Though last year, when I was completing the High Sierra Trail, my goal was Lone Pine Lake for the last night, but when I reached Outpost, my eyes and legs were burning. So I put up my tent, made dinner, crawled inside, and slept like Rip Van Winkle (as did all of my trail friends).
Now, as to weather. Generally, the best way to deal with afternoon storms is to get up early, watch what the clouds are doing as you climb, and summit before 12 noon or 1 if the conditions permit. That usually works (the weather very often does permit later summits, and sometimes does prevents noon summits, but the noon-1 p.m. benchmark is a reasonable rule of thumb). But as you probably saw from some trip reports, every year or two, Whitney gets a really violent weather situation, kind of a freak storm. And occasionally, as you see from the trip reports, it is not possible to get all the way to the Portal safely during the storm, and you which case you may have to be prepared hunker down for a few hours, or even the night, wherever you find yourself.
