As has already been mentioned, your problem is that $open is scoped locally to the sub open_file. This doesn't work, because that way the variable is not accessible outside of the sub (when you click the Get Statistics button).
Make it a global variable
my $open; # variable with file scope
# The sub open :
sub open_file {$open = $mw->getOpenFile( # no my here!
...
and then simply use the variable inside of get_statistics:
sub get_statistics {
...
my $fastaFile = $open;
...
Alternatively, use the variable $current_file. You do have assigned $open to it, but you are not using it anywhere...
sub get_statistics {
...
my $fastaFile = $current_file;
...