1. It is symbolic (although the last paragraph may have a Halachic effect, which we only give a one-year term on) and doesn’t accomplish any Halachic function so we do it every year.
2. In many places women do do it or appoint a brother/father/spouse as a Shaliach when they do it.
3. The answer would be the same as my answer to #1, though it’s not clear that a father or brother actually can serve on the Beis Din.