how access a method in the parent class that's been overridden in the child?

Prefix parent:: to the method name:
class shape {
    function draw( ) {
        // write to screen
    }
}

class circle extends shape {
   function draw($origin, $radius) {
      // validate data
      if ($radius > 0) {
          parent::draw( );
          return true;
      }

      return false;
   }
}

how execute different code depending on the number and type of arguments passed to a method?

PHP doesn't support method polymorphism as a built-in feature. However, you can emulate it using various type-checking functions. The following combine( ) function uses is_numeric(), is_string(), is_array(), and is_bool():
// combine() adds numbers, concatenates strings, merges arrays,
// and ANDs bitwise and boolean arguments
function combine($a, $b) {
    if (is_numeric($a) && is_numeric($b)) {
        return $a + $b;
    }

    if (is_string($a)  && is_string($b))  {
        return "$a$b";
    }

    if (is_array($a)   && is_array($b))   {
        return array_merge($a, $b);
    }

    if (is_bool($a)    && is_bool($b))    {
        return $a & $b;
    }

    return false;
}

want to link two objects, so when you update one, you also update the other?

Use =& to assign one object to another by reference:
$adam = new user;
$dave =& $adam;

how eliminate an object?

Objects are automatically destroyed when a script terminates. To force the destruction of an object, use unset( ):
$car = new car; // buy new car
...
unset($car);    // car wreck

how create a new instance of an object?

Define the class, then use new to create an instance of the class:
class user {
    function load_info($username) {
       // load profile from database
    }
}

$user = new user;
$user->load_info($_REQUEST['username']);

exchange the values in two variables without using additional variables for storage?

To swap $a and $b:
list($a,$b) = array($b,$a);

access the values passed to a function?how

Use the names from the function prototype:
function commercial_sponsorship($letter, $number) { 
    print "This episode of Sesame Street is brought to you by ";
    print "the letter $letter and number $number.\n";
}

commercial_sponsorship('G', 3);
commercial_sponsorship($another_letter, $another_number);

how associate multiple elements with a single key?

Store the multiple elements in an array:
$fruits = array('red' => array('strawberry','apple'),
                'yellow' => array('banana'));
Or, use an object:
while ($obj = mysql_fetch_object($r)) {
    $fruits[ ] = $obj;
}

How to check whether two floating-point numbers are equal?

Use a small delta value, and check if the numbers are equal within that delta:
$delta = 0.00001;

$a = 1.00000001;
$b = 1.00000000;

if (abs($a - $b) < $delta) { /* $a and $b are equal */ }

You want to extract part of a string, starting at a particular place in the string

Use substr( ) to select your substrings:
$substring = substr($string,$start,$length);
$username = substr($_REQUEST['username'],0,8);