No permits are required to hike up to Lower Boy Scout Lake on the North Fork (mountaineers route approach). On the Main Trail, not required to hike up to Lone Pine Lake.
The hike up the North Fork as far as you are talking is not much more than a "bush whack", only it is a pretty good trail for never being actually built as such. It goes through the trees and bushes, and has some steep climbing on the slope opposite the Ebersbacher Ledges. Other than getting up to look across at the granite, there isn't much of a "destination" objective to do what you propose. A good view of Mt Whitney doesn't come until you are almost to LBSL.
As for question 2, the stream crossing is the biggest obstacle. I think the "trail" splits at one point where you can climb that steep slope, but both splits climb it.
I took my 11-Y-O daughter up the E-Ledges last May to Lower Boy Scout, and she thoroughly enjoyed it, but then she really loves heights and exposure. We ate lunch at LBSL and then returned to Whitney Portal.
It would be a more rewarding hike to hike to Lone Pine Lake, since it offers a pretty lake where you can stop. Though it would take longer. Your detour up the North Fork and back might take one (2 maximum) hour from the Main Trail.
