If the #! line isn't correct then your code will be passed to /bin/sh, not Perl

No.

$ a.pl
sh: ./a.pl: usr/bin/perl: bad interpreter: No such file or directory
[download]

and that's what produced the error messages.

No. If the error messages originated from sh, they would look like

$ . a.pl
sh: =: command not found
sh: ./a.pl: line 3: syntax error near unexpected token `{'
sh: ./a.pl: line 3: `if ($count <= 20) {'
[download]

or (requires changing shebang to #!/bin/sh)

$ a.pl
./a.pl: line 2: =: command not found
./a.pl: line 3: syntax error near unexpected token `{'
./a.pl: line 3: `if ($count <= 20) {'
[download]

The error the OP gave is indeed from perl.