Permitting and route question

Considering a mid-July route in the Mineral King area heading up Timber Gap/Cliff Creek to Hamilton Lakes, over the Kaweah Gap, to Little Five Lakes, Big Five Lakes and back over Sawtooth Pass. 44 miles in 5-6 days. Question 1: About 10 miles of the loop is on the High Sierra Trail. So do I only need the Timber Gap permit, or do I also need a permit for the High Sierra Trail?

Question 2: Thoughts on the loop in general, mainly from a weather/storms risk standpoint? We’re a capable group with experience hiking in the Northeast primarily, and understand the risks of thunderstorms well. This route would have a couple of nights camping in alpine environments. In case of inclement weather, what is the cover like up there?