Extract First Character (allowing for extra grouping)

You should use the \StrRemoveBraces before \StrChar:

\newcommand*{\ExtractFirstChar}[1]{%
    \StrRemoveBraces{#1}[\FirstChar]%
    \StrChar{\FirstChar}{1}[\FirstChar]%
    First char of '#1' is '\FirstChar'\par
}

Assuming your input only contains (non TeX special) ASCII characters and braces:

\documentclass{article}
\usepackage{xparse}

\ExplSyntaxOn
\NewExpandableDocumentCommand{\firstchar}{sm}
 {
  \IfBooleanTF{#1}
   {
    \grill_firstchar:V #2
   }
   {
    \grill_firstchar:n { #2 }
   }
 }

\cs_new:Nn \grill_firstchar:n
 {
  \int_compare:nTF { \tl_count_tokens:f { \tl_head:n { #1 } } > 1 }
   {% we have to redo
    \grill_firstchar:f { \tl_head:n { #1 } }
   }
   {% just one token
    \tl_head:n { #1 }
   }
 }
\cs_generate_variant:Nn \tl_count_tokens:n { f }
\cs_generate_variant:Nn \grill_firstchar:n { V, f }

\ExplSyntaxOff

\begin{document}

\firstchar{abc} should print ``a''

\firstchar{{a,b,c}} should print ``a''

\firstchar{{{a},b,c}} should print ``a''

\newcommand\test{{{a}},b,c}

\edef\result{\firstchar*{\test}} \result\ should print ``a''

\end{document}