is it possible to count the number of keys in a hash?

Yes it is, using the keys operator in scalar context:

my $number_of_keys_in_hash = keys %hash;
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%hash = (
for($b=0;$b<$cnt;$b++){$a=$b+1; #$cnt being the number of keys in the 
+hash
$new"."$a="new_input_from_form"."$a";#. form is in a .pl file
if($new"."$a ne ""){$new_key_and_value="'$a' => '$new"."$a',";} #use v
+alue from the form in the hash
elsif($new"."$a eq ""){$new_key_and_value="'$a' => '$hash{'$a'}',";} #
+use the old value from the exi
+sting hash

$new_key_and_value

}#close the for loop

); #close the hash
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You can't enclose multiple statements inside parentheses, they don't work like that.    You have to use a code block of some kind.

The expression  $new"."$a makes no sense.    There is no operator between the $new variable and the string "." and between the string and the $a variable.

The $b variable is only there to set the value of the $a variable so why use it at all?    And you really shouldn't use the $a and $b variables at all.