Uniform Unicode for text, math and listings?

Question

What should I put in the preamble (preferably packages) for this to work as expected with its unicode characters?

\documentclass{article}
\usepackage{listings}
\begin{document}
  $α$ α
  \begin{lstlisting}
     α = 1.;
  \end{lstlisting}
\end{document}

Note that alpha (α) appears in three contexts: as text, as math and as code (listings).

(I can use lualatex if it simplifies things)

---

For a higher challenge, in this case I introduce a second level of difficulty, by introducing a second kind of alpha (𝛼: 0x1d6fc Mathematical italic small alpha vs. α: Greek small letter alpha). To see to what degree TeX can deal with the nuance (e.g. by make 𝛼 into $\alpha$, or by making 𝑝 --0x1D45D Mathematical italic small p-- into $p$):

\documentclass[]{article}
\usepackage[]{listings}
\begin{document}
$α$ α $𝛼$ 𝛼 𝑝
\begin{lstlisting}
α = 1.
𝛼 = 2.
\end{lstlisting}
\end{document}

Answer 1

For the listings part of the question, you'll need something like the following (adapting the answers from the questions that @morbusg pointed to). This works in xelatex. I agree with @morbusg that the tricky part will be to find fonts that contain your glyphs, especially typewriter and math fonts.

\documentclass{article}
\usepackage{fontspec}
\setmainfont{FreeSerif}
\usepackage{listings}
\lstset{inputencoding=utf8,extendedchars=true}
\makeatletter
\lst@InputCatcodes
\def\lst@DefEC{%
 \lst@CCECUse \lst@ProcessLetter
  ^^^^03b1% α
  ^^^^^^01d6fc% 𝛼
  ^^^^^^01d45d% 𝑝
  ^^00}
\lst@RestoreCatcodes
\makeatother
\begin{document}
\begin{lstlisting}
α = 1.
𝛼 = 2.
𝑝 = 3.
\end{lstlisting}
\end{document}

Answer 2

You can use unicode-math and fontspec packages for use with xelatex and lualatex, but unfortunately listings doesn't work with unicode so it has been suggested on this site to use packages like minted instead. (UTF8 for listings, The 'listings' package and UTF-8, Having problems with listings and UTF-8. Can it be fixed?, verbments (listings alternative) and UTF-8, UTF-8 (BMP character set) support in listings., etc. etc.)

But otherwise:

\documentclass{article}
\usepackage{fontspec,unicode-math}
\setmainfont{Cambria}
\setmathfont{Cambria Math}
\setmonofont{Consolas}
\begin{document}
$\alpha$, $α$, $𝛼$, α
\end{document}

Note that text fonts don't include (all of) the mathematical glyphs. Especially not the mathematical alphanumeric range.