One way you can validate the fields is by adding a method to:
woocommerce_checkout_process
So that in your functions.php you add a method, for example:
add_action('woocommerce_checkout_process', 'validatePhone');
function validatePhone() {
$billing_phone = filter_input(INPUT_POST, 'billing_phone');
if (strlen(trim(preg_replace('/^[6789]\d{9}$/', '', $billing_phone))) > 0) {
wc_add_notice(__('Número telefónico incorrecto.'), 'error');
}
}
Another way to do it through the functions.php is to add your own Woocommerce fields.
Regarding your new question @Walworth to validate only letters you can change the regular expression or use the ctype_alpha ctype_alpha returns a value TRUE if its argument is a text string if you still decide to use a regular expression you can use:
if(preg_match('/^[a-zA-Z]+$/', $var)) //$var es la cadena a evaluar y retorna true si lo es