The ® character is not processed correctly in my form

Question 1

character encoding plays a rule at multiple places in your scenario

which encoding does the client use for sending the parameters to the server
which encoding does the mysql server use to intepret characters send from the php script to the server
which encoding does the mysql server use to send results back to the php script
which encoding does the mysql server use to store the data
which encoding does the client/browser use to render the data send from the php script to the client/browser

It's simplest to keep the whole chain at utf-8 encoding:
Set the character encoding of the html documents you send to the browser to utf-8, e.g. via default_charset.
Indicate to the mysql server that the connection charset is utf-8, e.g. via setting the charset property in the PDO-MYSQL DSN.
Create the table using utf-8 as default charset and without specifiying another encoding for the field itself.

Self-contained example:

<?php
ini_set('default_charset', 'utf-8');
$fn = isset($_POST['val']) ? 'doDatabase' : 'doForm';
doHtml($fn);


function doHtml($fn) { ?>
<html>
    <head><title>...</title></head>
    <body>
        <?php $fn(); ?>
    </body>
</html>
<?php
}

function doForm() { ?>
    <form method="POST" action="?">
        <div>
            <input type="text" name="val" value="&reg;" />
            <input type="submit" />
        </div>
    </form>
<?php       
}

function doDatabase() {
    $pdo = new PDO('mysql:host=localhost;dbname=test;charset=utf8', 'localonly', 'localonly');
    $pdo->setAttribute(PDO::ATTR_ERRMODE, PDO::ERRMODE_EXCEPTION);
    $pdo->setAttribute(PDO::ATTR_EMULATE_PREPARES, false);

    $pdo->exec('
        CREATE TEMPORARY TABLE soFoo (
            id int auto_increment,
            val varchar(30),
            primary key(id)
        ) DEFAULT CHARACTER SET utf8
    ');

    $stmt   = $pdo->prepare('INSERT INTO soFoo (val) VALUES (?)');
    $stmt->execute( array($_POST['val']) );
    $stmt = null;

    foreach( $pdo->query('SELECT * FROM soFoo', PDO::FETCH_ASSOC) as $row ) {
        echo 'row: ', join(', ', $row), "<br />\r\n";
    }
}

Question 2

You should try mysql5 table with the utf8_general_ci collation