Mail form through php - php

Question

I have made this form and I want to ask is this safe enough. I tried many times making a captcha thingie but it won't work for me. I am still a student please don't sent to hard things.
Question 1 : Is mysql_real_escape_string safe enough?
Question 2 : I need a really simple (numeric) captcha, can someone send me an example (or other stack post)
This gona be used on an informatic site just as a mail form. on that site are no databases/logins and that.
<?php
include '../connect.php'; #db connection for mysql_real_escape_string
$errors = array('');
//valideren of er op de submit gedrukt is en of alle benodigde data is ingevuld
if(isset($_POST['submit'])){
if(!empty($_POST['naam']) && !empty($_POST['email']) && !empty($_POST['bericht'])){
$naam = mysql_real_escape_string($_POST['naam']);
$email = mysql_real_escape_string($_POST['email']);
$bericht = mysql_real_escape_string($_POST['bericht']);
$telefoon = mysql_real_escape_string($_POST['telefoon']);
$regex = "/^[A-Za-z .'-]+$/";
if(!preg_match($regex,$naam)) {
array_push($errors , 'De naam is niet geldig');
}
if(strlen($bericht) < 5) {
array_push($errors , 'Het bericht is te kort');
}
$email_regex = '/^[A-Za-z0-9._%-]+#[A-Za-z0-9.-]+\.[A-Za-z]{2,4}$/';
if(!preg_match($email_regex,$email)) {
array_push($errors , 'Uw email is niet geldig.');
}
Here comes mail part.
}else{
array_push($errors , 'Een van de verplichte velden is niet ingevuld. Alle velden met * zijn verplicht.');
}
}
?>
<form method="post">
<p>
<label>naam*</label>
<input type="text" name="naam"/>
</p>
<p>
<label>email*</label>
<input type="text" name="email"/>
</p>
<p>
<label>telefoon</label>
<input type="text" name="telefoon"/>
</p>
<p>
<label>Bericht*</label>
<textarea name="bericht" style="width:459px; height:187px;" ></textarea>
</p>
<p>
<label> </label>
<input type="submit" value="verstuur" name="submit"/>
</p>
</form>
<?php
if (count ($errors > 0)){
foreach($errors as $error){
echo '<p class="error">'.$error.'</p>';
}
}
?>

Answer 1

Is mysql_real_escape_string safe enough?
It is a poor solution for protecting a MySQL database.
It is completely inappropriate for sending email.
Whatever you do to protect bad data from corrupting your email, it should be done just before the data is inserted into that email — not before you run sanity checks over it.