1. How do you give functions private variables that retain their values between calls?

Create a scope surrounding that sub that contains lexicals.
Only lexical variables are truly private, and they will persist even when their block exits if something still cares about them. Thus:
{ my $i = 0; sub next_i { $i++ } sub last_i { --$i } }
creates two functions that share a private variable. The $i variable will not be deallocated when its block goes away because next_i and last_i need to be able to access it.

2. How many ways can we express string in Perl?

Many. For example 'this is a string' can be expressed in:
"this is a string"
qq/this is a string like double-quoted string/
qq^this is a string like double-quoted string^
q/this is a string/
q&this is a string&
q(this is a string)

3. How do I print the entire contents of an array with Perl?

To answer this question, we first need a sample array. Let's assume that you have an array that contains the name of baseball teams, like this:
@teams = ('cubs', 'reds', 'yankees', 'dodgers');
If you just want to print the array with the array members separated by blank spaces, you can just print the array like this:
@teams = ('cubs', 'reds', 'yankees', 'dodgers');
print "@teamsn";
But that's not usually the case. More often, you want each element printed on a separate line. To achieve this, you can use this code:
@teams = ('cubs', 'reds', 'yankees', 'dodgers');
foreach (@teams) {
print "$_n";
}

4. How do you match one letter in the current locale?

/[^W_d]/
We don't have full POSIX regexps, so you can't get at the isalpha() <ctype.h> macro save indirectly. You ask for one byte which is neither a non-alphanumunder, nor an under, nor a numeric. That leaves just the alphas, which is what you want.

5. Assume that $ref refers to a scalar, an array, a hash or to some nested data structure. Explain the following statements:

$$ref; # returns a scalar
$$ref[0]; # returns the first element of that array
$ref- > [0]; # returns the first element of that array
@$ref; # returns the contents of that array, or number of elements, in scalar context
$&$ref; # returns the last index in that array
$ref- > [0][5]; # returns the sixth element in the first row
@{$ref- > {key}} # returns the contents of the array that is the value of the key "key"

6. What happens to objects lost in "unreachable" memory..... ?

What happens to objects lost in "unreachable" memory, such as the object returned by Ob->new() in `{ my $ap; $ap = [ Ob->new(), $ap ]; }' ?

Their destructors are called when that interpreter thread shuts down.
When the interpreter exits, it first does an exhaustive search looking for anything that it allocated. This allows Perl to be used in embedded and multithreaded applications safely, and furthermore guarantees correctness of object code.

7. When would local $_ in a function ruin your day?

When your caller was in the middle for a while(m//g) loop
The /g state on a global variable is not protected by running local on it. That'll teach you to stop using locals. Too bad $_ can't be the target of a my() -- yet.

8. How do I read command-line arguments with Perl?

With Perl, command-line arguments are stored in the array named @ARGV.
$ARGV[0] contains the first argument, $ARGV[1] contains the second argument, etc.
$#ARGV is the subscript of the last element of the @ARGV array, so the number of arguments on the command line is $#ARGV + 1.
Here's a simple program:
#!/usr/bin/perl
$numArgs = $#ARGV + 1;
print "thanks, you gave me $numArgs command-line arguments.n";
foreach $argnum (0 .. $#ARGV) {
print "$ARGV[$argnum]n";
}

9. How to concatenate strings with Perl?

Method #1 - using Perl's dot operator:
$name = 'checkbook';
$filename = "/tmp/" . $name . ".tmp";

Method #2 - using Perl's join function
$name = "checkbook";
$filename = join "", "/tmp/", $name, ".tmp";

Method #3 - usual way of concatenating strings
$filename = "/tmp/${name}.tmp";

10. What is the easiest way to download the contents of a URL with Perl?

Once you have the libwww-perl library, LWP.pm installed, the code is this:
#!/usr/bin/perl
use LWP::Simple;
$url = get 'http://www.websitename.com/';