How to move nodes's names and emphasize arrow tips?

Question

I am trying to draw a Cayley graph for Z_8 and need some arrows. My problems :

1. The names of nodes come exactly on the coordinators, is there a way of setting it to appear beside the coordinator not on it. Or, how can I move it manually up and down?
2. Because I fullback the nodes, the tips of arrows don't appear clearly. How can I solve it, even If I had to put the tip in the middle of the arrow. I appreciate any help or suggestions.

MWE:

\documentclass[12pt,letter]{article}

\usepackage{xcolor}
\usepackage{graphicx}


\usepackage{tikz}
\usetikzlibrary{arrows,shapes,positioning,mindmap,trees,automata}
\usepackage{amsfonts,amsmath,amsthm,epsf,graphics,verbatim,amssymb,amscd,eucal,bbm} 
\newcommand{\Z}{{\mathbb Z}}
\begin{document}
\begin{figure}[h]
\begin{center} 
  \begin{tikzpicture}[line width=2pt]
  %\draw [blue](2,.5) -- (3,.5) ; \draw [blue](-2,.5) -- (-3,.5) ;
%    
%    \draw[style1] (0,0) -- ++( 1,0) coordinate (x);
%\draw[style2] (x)   -- ++( 0,1) coordinate (x);
%\draw[style3] (x)   -- ++(-1,0);
%    

\draw[->,thick] (-1,1.8) -- (-2,.5); 
\draw[->,thick, dashed](1,1.8)  -- (2,.5){}; 
%\draw[bend right,->,thin]  (1) to node [sloped,below] {$\mu(b)$} (3);
%\draw[bend right,->,thin]  (1) to node [sloped,above] {$\mu(a)$} (4);
%    
  \node (A) at (-1,1.8) {\;\;0};
\node (B) at (1,1.8) {\;\;1};
\draw[bend left,->,thin]  (A) to node [auto] {} (B);
%    \draw[->, to path={-| (\tikztotarget)}]

  (A) edge (B);% (B) edge (C)  (C) edge (D);
  \draw[fill=black] (-1,1.8) circle (0.1) ;
\draw[fill=black] (1,1.8) circle (0.1) ; 
\draw[fill=black] (-2,.5) circle (0.1) ;

\draw[fill=black] (-2,-.8) circle (0.1) ;
\draw[fill=black] (2,.5) circle (0.1) ;

\draw[fill=black] (2,-.8) circle (0.1) ;
\draw[fill=black] (-1,-2.1) circle (0.1) ;
\draw[fill=black] (1,-2.1) circle (0.1) ; 


\end{tikzpicture}
\end{center} 
\caption{Cayley graphs on $\Z_8$ with generators set: $\{2,3\}$}
\label{polya Z^2}
 \end{figure}   

 \end{document}  

Answer 1

Using proper nodes of style dot you can put circles on the paper and connecting lines will automatically stop at their border – that's the point of nodes.

A label which is just another node can be placed in relation to that node.

%\documentclass[12pt, tikz]{standalone}
\documentclass[12pt, letter]{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}[
  line width=2pt,
  dot/.style={circle, inner sep=+0pt, draw, fill, minimum size=+2mm}
]
\foreach \i in {0, ..., 3}
  \foreach[
    count=\jj from 0,
    evaluate={\n=int(2*\i+\jj);},
  ] \j in {25, 65}
    \node[dot, label={[circle,inner sep=+.15em]\j+90*\i:$\n$}]
      (n-\n) at (\j+90*\i:2) {};
\path (n-0) edge[dashed]           (n-1)
      (n-2) edge                   (n-3)
            edge[->, bend left=45] (n-1)
      ;
\end{tikzpicture}
\end{document}

Output