1. Walk in, find an empty pad, claim it. There is a kiosk where you fill out an envelope and insert cash. That's it.
2. Overnight: If you come down the main trail, that means you have to haul all your overnight gear to the summit. Most people who do that will spend a night on the summit. But you then also need a Trail Crest Exit permit in addition to your North Fork overnight permit.
If you day hike the Mountaineers Route, you can then descend the Main Trail -- day use permits are for anywhere in the Whitney Zone, it is the same permit as the Main Trail day use permit.
3. You can day hike up to Lower Boy Scout Lake and back without a permit. Same for Lone Pine Lake on the Main Trail.