Yes there is. When you have a new repository without any commits, there is no HEAD, so you can't unstage by resetting.

    mkdir try
    cd try
    git init
    touch file
    git add file
    git status

Still, the git status command shows you what you need to do to unstage.

Indeed no. That's exactly what git reset does: "copy entries from <commit> to the index". I got that from the unusably bad man page. It was the first sentence.

I forget my exact edge case. Something to do with wanting to unstage a folder, or unstaging a folder while wanting to preserve work in some of the files.