Define macros by using TikZ's \foreach

You can do without TikZ, and, what may be more important, avoid making the macros global. You can use the built-in \@for macro instead.

\documentclass{article}
\makeatletter
\@for\next:={above,below,right,left}\do{%
\expandafter\edef\csname test\next\endcsname#1{\next #1}}
\makeatother
\begin{document}
\testabove{A}     
\testbelow{B}     
\testright{C} 
\testleft{D}
\end{document}

There are many ways in which you may generalize this and/or make it more user-friendly. I do not know what the ultimate purpose will be, but this is to give you some idea.

\documentclass{article}
\makeatletter
\newcommand{\MultiDef}[3][]{\@for\next:=#3\do{%
\expandafter\edef\csname #2\next\endcsname##1{#1{\next} ##1}}}
\makeatother
\begin{document}
\MultiDef{test}{above,below,right,left}
\testabove{A}     
\testbelow{B}     
\testright{C} 
\testleft{D}

\MultiDef[hibernate ]{pft}{above,below,right,left}
\pftabove{A}     
\pftbelow{B}     
\pftright{C} 
\pftleft{D}
\end{document}

The \foreach function is meant for repetitive actions in TikZ pictures and has several drawbacks when employed elsewhere, the main one being that every cycle is performed in a group.

Here's a more general way to accomplish your needs; the defined macros can have as many arguments as you like (from none to nine, of course). In the fourth argument (the template) you denote by #1 the current item in the cycle and by ##1, ##2 and so on the defined macro arguments.

\documentclass{article}
\usepackage{xparse}

\ExplSyntaxOn

\NewDocumentCommand{\batchdefine}{mO{0}mm}
 {% #1 is the prefix
  % #2 (default 0) is the number of arguments
  % #3 is a comma separated list
  % #4 is the template
  \clist_map_inline:nn { #3 } 
   {
    \projetmbc_batchdefine:cnn { #1 ##1 } { #2 } { #4 }
   }
 }

\cs_new_protected:Nn \projetmbc_batchdefine:Nnn
 {
  \newcommand{#1}[#2]{#3}
 }
\cs_generate_variant:Nn \projetmbc_batchdefine:Nnn { c }

\ExplSyntaxOff

\batchdefine{test}[1]{
  above, below, right, left
}{#1 ##1}

\batchdefine{TEST}[2]{
  above, below, right, left
}{##1 #1 ##2}

\begin{document}

\testabove{a} \testbelow{b} \testright{r} \testleft{l}

\TESTabove{a}{A} \TESTbelow{b}{B} \TESTright{r}{R} \TESTleft{l}{L}

\end{document}

Thanks to the comments of Phelype Oleinik and LaTeXer, the following solution has been build.

\documentclass[12pt]{article}

\usepackage{tikz}

\foreach \kind in {above,below,right,left}{
    \expandafter\xdef\csname test\kind\endcsname##1{\kind ##1}
}


\begin{document}

\testabove{A} ;    
\testbelow{B} ;    
\testright{C} ;    
\testleft{D}

\end{document}