Both questions are answered in git status
.
To unstage adding a new file use git rm --cached filename.ext
# Changes to be committed:
# (use "git rm --cached <file>..." to unstage)
#
# new file: test
To unstage deleting a file use git reset HEAD filename.ext
# Changes to be committed:
# (use "git reset HEAD <file>..." to unstage)
#
# deleted: test
In the other hand, git checkout --
never unstage, it just discards non-staged changes.