Golden Ratio for vertical poem positioning

The following code shows the answer to your first question (before your edit):

\documentclass[11pt]{article}
\usepackage[utf8]{inputenc}
\usepackage{tikz}
\usetikzlibrary{calc,positioning}
\def\Poem#1#2#3#4{ % width, title, content, author
\begin{tikzpicture}[overlay, remember picture]
\node[text width=#1] (poem) 
    at ($(current page.south)!.61803399!(current page.north)$)
    {#3};
\node[below=of poem.south east, left] {\emph{#4}};
\node[above=of poem.north west, right] {\textbf{\textsf{{\Large#2}}}};
\end{tikzpicture}
\newpage
}

\def\ShowMarks{ % draws frame around page, and horizontal rule at golden ratio
\begin{tikzpicture}[overlay, remember picture,red]
\draw (current page.south west) rectangle (current page.north east);
\draw ($(current page.south west)!.61803399!(current page.north west)$) --
      ($(current page.south east)!.61803399!(current page.north east)$);
\end{tikzpicture}
}


\begin{document}
\ShowMarks{}%
\Poem{7cm}{Abendlied}{%
    Über allen Gipfeln\\
    Its Ruh,\\
    In allen Wipfeln\\
    Spürest du\\
    Kaum einen Hauch;\\
    Die Vögelein schweigen im Walde\\
    Warte nur, balde\\
    Ruhest Du auch.\\
}{Johan Wolfgang von Goethe}
\end{document}

Resulting in (you have to compile twice, it is the way absolute TikZ positioning works):

UPDATE To answer the second question, a new anchor should be defined so that, instead of being in the center of the poem, it is in a "golden ratio" point inside it. This is tricky, but can be done. However, note that the width of the poem has to be specified beforehand, and if you specify a width which is not tight, all the golden-ratio calculations are pointless.

This is my solution (I included a blue shade to see the poem box, you can disable it removing the fill=blue!20 option):

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{tikz}
\usetikzlibrary{calc,positioning}
\makeatletter
\pgfdeclareshape{golden anchored}
{
  \inheritsavedanchors[from=rectangle] % this is nearly a rectangle 
  \inheritanchorborder[from=rectangle]
  \inheritanchor[from=rectangle]{center}
  \inheritanchor[from=rectangle]{north}
  \inheritanchor[from=rectangle]{north east}
  \inheritanchor[from=rectangle]{north west}
  \inheritanchor[from=rectangle]{south}
  \inheritanchor[from=rectangle]{south east}
  \inheritanchor[from=rectangle]{south west}
  \inheritanchor[from=rectangle]{west}
  \inheritanchor[from=rectangle]{east}
  \inheritbackgroundpath[from=rectangle]
  \savedanchor{\goldenpoint}{
    \pgf@y=1\ht\pgfnodeparttextbox
    \advance\pgf@y by 1\dp\pgfnodeparttextbox
    \pgf@y=.61803399\pgf@y
    \advance\pgf@y by -1\dp\pgfnodeparttextbox
    \pgf@x=.381966011\wd\pgfnodeparttextbox
  }
  \anchor{golden}{ \goldenpoint }
  \anchor{text}{\pgfpoint{0}{0}}
}
\makeatother

\def\Poem#1#2#3#4{ % width, title, content, author
\begin{tikzpicture}[overlay, remember picture]
\node[text width=#1, golden anchored, anchor=golden, fill=blue!20] (poem)
    at ($(current page.south)!.61803399!(current page.north)$)
    {#3};
\node[below=of poem.south east, left] {\emph{#4}};
\node[above=of poem.north west, right] {\textbf{\textsf{{\Large#2}}}};
\end{tikzpicture}
\newpage
}

\def\ShowMarks{ % draws frame around page, and horizontal rule at golden ratio
\begin{tikzpicture}[overlay, remember picture,red]
\draw (current page.south west) rectangle (current page.north east);
\draw ($(current page.south west)!.61803399!(current page.north west)$) --
      ($(current page.south east)!.61803399!(current page.north east)$);
\draw (current page.south) -- (current page.north);
\end{tikzpicture}
}
\begin{document}
\Poem{5.5cm}{Abendlied}{%
    Über allen Gipfeln\\
    Its Ruh,\\
    In allen Wipfeln\\
    Spürest du\\
    Kaum einen Hauch;\\
    Die Vögelein schweigen im Walde\\
    Warte nur, balde\\
    Ruhest Du auch.\\
\ShowMarks{}%
}{Johan Wolfgang von Goethe}
\end{document}

And the result (remember compiling twice):