Most people do it clockwise but it doesn't matter.

You don't have to do the whole thing. If you come in the Colorado side its mostly a good dirt road so it's an easy out and back.

but you don't have to wait 6 months to get the day use permits, you can just walk up most of the time. you can get permits all the time even for the backcountry sites it just goes quickly because there are some strong preferences for campsites and people want to have their itineraries locked down. if you're planning to bike it you can have some rough days if your sites don't line up in a reasonable way. even in the busy season you can grab 1 day campsite permits if you want to come middle of the week or something like that.mostly it's only hard to get permits because everybody wants to come when the weather is nice and for a long weekend trip.

it's not that fun to do as a day trip, there are better ways to spend your time even if you just want to have some good views. but if you're just driving in to a trailhead or something like that you don't have to plan the same way.

The permit is for backcountry camping. The weather is also pretty intense so everybody tries to go at the same time of year.

Correct. It's Skyline Rim.