Grand Canyon: Tanner Trail - Beamer Trail - Colorado River/Little Colorado River Confluence 

Permits are required to enter the Havasupai Falls area. As long as you have a permit, I don't believe there would be an issue entering from the LCR, but you would likely want to verify that with the tribe.

You are talking about two different places. The Little Colorado River and Havasu Creek are separated by dozens of miles of canyon and are not close to each other at all. The Salt Trail is difficult but doable and will take you to the LCR and permits are much more accessible - Havasu area permits are much more difficult to get and you must apply months-years in advance (The Salt Trail and LCR area is managed by the Navajo Nation, the Havasu area is managed by the Havasupai people). You can filter out of either watershed by the water tastes odd and can give some headaches due to high mineral content.

Taste in music is subjective.

The hike starts at Lipan Point from the South Rim near the Desert View Watchtower. I've attached a trip description link. The trip is approximately 37 miles (round trip). We did this as a 4-day, 3-night backpack. Definitely not a hike for 'children', unless we're talking about adult children. www.backpacker.com/trips/grand-canyon-national-park-tanner-and-beamer-trails-to-little-colorado-river/