I disagree. A manager is not an individual contributor. It's important for them to have technical skills, but I don't think it's necessary they be on par with an average developer, let alone better than the best.
Absolutely disagree. They need enough technical skills to understand gist of what is going on, but beyond that they should be deferring to the people on the team with the most relevant experience/expertise in technical questions.
The most important skill my boss can have is the ability to sweet talk his boss.
* The developers they're managing.