> Can a Perl module "inspect" itself and provide details about methods..

Yes! You can parse a perl document with PPI two oneliners just to get started:

# a bare package provided as string

perl -MPPI -e "print $_->content for @{ PPI::Document->new(\'package M
+yPack{ sub new{ bless{}, shift} }')->find('PPI::Statement::Sub') }"

#output
sub new{ bless{}, shift}


# inspecting Data::Dump module (getting its path from %INC)

perl -MPPI -MData::Dump -e "print $_->content for @{ PPI::Document->ne
+w( $INC{'Data/Dump.pm'} )->find('PPI::Statement::Sub') }; "

#output

sub dump
{
    local %seen;
    local %refcnt;
    local %require;
    local @fixup;
...
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You can go further trying to extract arguments received (good luck ;) and maybe you have to learn what PPI PDOM Tree is:

perl -MPPI -MPPI::Dumper -e "PPI::Dumper->new( PPI::Document->new(\'pa
+ckage MyPack{ sub new{my class shift; return bless{},$class}  }') )->
+print"

PPI::Document
  PPI::Statement::Package
    PPI::Token::Word    'package'
    PPI::Token::Whitespace      ' '
    PPI::Token::Word    'MyPack'
    PPI::Structure::Block       { ... }
      PPI::Token::Whitespace    ' '
      PPI::Statement::Sub
        PPI::Token::Word        'sub'
        PPI::Token::Whitespace          ' '
        PPI::Token::Word        'new'
        PPI::Structure::Block   { ... }
          PPI::Statement::Variable
            PPI::Token::Word    'my'
            PPI::Token::Whitespace      ' '
            PPI::Token::Word    'class'
            PPI::Token::Whitespace      ' '
            PPI::Token::Word    'shift'
            PPI::Token::Structure       ';'
          PPI::Token::Whitespace        ' '
          PPI::Statement::Break
            PPI::Token::Word    'return'
            PPI::Token::Whitespace      ' '
            PPI::Token::Word    'bless'
            PPI::Structure::Constructor         { ... }
            PPI::Token::Operator        ','
            PPI::Token::Symbol          '$class'
      PPI::Token::Whitespace    '  '
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L*