Customized form-login.php template file in Child Theme – Add Validation and Save

I have a child theme that I am attempting to add additional form fields on the registration form. I followed the direction in How to add custom fields in user registration on the “My Account” page resulting in the following function:

/**
 * Add new register fields for WooCommerce registration.
 *
 * @return string Register fields HTML.
 */
// Function to check starting char of a string
function startsWith($haystack, $needle){
	return $needle === '' || strpos($haystack, $needle) === 0;
}

// Custom function to display the Billing Address form to registration page
function my_custom_function(){
	global $woocommerce;
	$checkout = $woocommerce->checkout();

	foreach ($checkout->checkout_fields['billing'] as $key => $field) :
		if(!($key == 'billing_first_name' || $key == 'billing_last_name')){
			$field['required'] = false;
		}
		if(!($key == 'billing_email')){
			woocommerce_form_field( $key, $field, $checkout->get_value( $key ) );
		}
	endforeach;
		?>
	<br/>
	<?php
	$checked = $checkout->get_value( 'newsletter_opt_in1' ) ? $checkout->get_value( 'newsletter_opt_in1' ) : 1;
    woocommerce_form_field("newsletter_opt_in1", array(
		'type'              => 'checkbox',
		'class'             => array('form-row-wide input-checkbox'),
		'label'             => 'I would like to recieve the newsletter',
		'description'       => '',
		'default'           => ''
	), $checked );
}
add_action('woocommerce_register_form','my_custom_function');

// Custom function to save Usermeta or Billing Address of registered user
function save_address($user_id){
	global $woocommerce;
	$address = $_POST;
	foreach ($address as $key => $field) :
		if(startsWith($key,'billing_')){
			// Condition to add firstname and last name to user meta table
			if($key == 'billing_first_name' || $key == 'billing_last_name'){
				$new_key = explode('billing_',$key);
				update_user_meta( $user_id, $new_key[1], $_POST[$key] );
			}
			update_user_meta( $user_id, $key, $_POST[$key] );
		}
	endforeach;

	if ( isset( $_POST['newsletter_opt_in'] ) ) {
		update_user_meta( $user_id, 'newsletter_opt_in', $_POST['newsletter_opt_in']);
	}
}
add_action('woocommerce_created_customer','save_address');

/**
 * Validate the extra register fields.
 *
 * @param  string $username          Current username.
 * @param  string $email             Current email.
 * @param  object $validation_errors WP_Error object.
 *
 * @return void
 */
function wooc_validate_extra_register_fields( $username, $email, $validation_errors ) {
	if ( isset( $_POST['billing_first_name'] ) && empty( $_POST['billing_first_name'] ) ) {
		$validation_errors->add( 'billing_first_name_error', __( 'First name is required!', 'woocommerce' ) );
	}

	if ( isset( $_POST['billing_last_name'] ) && empty( $_POST['billing_last_name'] ) ) {
		$validation_errors->add( 'billing_last_name_error', __( 'Last name is required!.', 'woocommerce' ) );
	}
}

add_action( 'woocommerce_register_post', 'wooc_validate_extra_register_fields', 10, 3 );

The issue I have with this approach is that unless I add the above code blocks to the parent functions.php file the additional fields do no show.

Therefore, I decided to modify the form-login.php file and add it to my child theme with the following code block:

<p class="form-row form-row-first">
               <label for="reg_billing_first_name" class=""><?php _e( 'First Name', 'woocommerce' ); ?><span class="required" title="required">*</span></label>
               <input type="text" class="input-text " name="billing_first_name" id="reg_billing_first_name" value="<?php if ( ! empty( $_POST['billing_first_name'] ) ) echo esc_attr( $_POST['billing_first_name'] ); ?>">
           </p>

           <p class="form-row form-row-last">
				<label for="reg_billing_last_name" class=""><?php _e( 'Last Name', 'woocommerce' ); ?><span class="required" title="required">*</span></label>
                <input type="text" class="input-text " name="billing_last_name" id="reg_billing_last_name" value="<?php if ( ! empty( $_POST['billing_last_name'] ) ) echo esc_attr( $_POST['billing_last_name'] ); ?>">
           </p>

           <div class="clear"></div>

           <p class="form-row form-row-wide">
           		<label for="reg_billing_company" class=""><?php _e( 'Company Name', 'woocommerce' ); ?></label>
                <input type="text" class="input-text " name="billing_company" id="reg_billing_company" value="<?php if ( ! empty( $_POST['billing_company'] ) ) echo esc_attr( $_POST['billing_company'] ); ?>">
		   </p>

           <p class="form-row form-row-wide">
           		<label for="reg_billing_phone" class=""><?php _e( 'Phone', 'woocommerce' ); ?></label>
                <input type="tel" class="input-text " name="billing_phone" id="reg_billing_phone" value="<?php if ( ! empty( $_POST['billing_phone'] ) ) echo esc_attr( $_POST['billing_phone'] ); ?>">
           </p>

           <div class="clear"></div>

<?php
  $suffix = defined( 'SCRIPT_DEBUG' ) && SCRIPT_DEBUG ? '' : '.min';
  $assets_path = str_replace( array( 'http:', 'https:' ), '', WC()->plugin_url() ) . '/assets/';
  $frontend_script_path = $assets_path . 'js/frontend/';

  wp_enqueue_script( 'wc-country-select', $frontend_script_path . 'country-select' . $suffix . '.js' );
				wp_enqueue_script( 'wc-address-i18n', $frontend_script_path . 'address-i18n' . $suffix . '.js' );
				wp_enqueue_script( 'wc-password-strength-meter', $frontend_script_path . 'password-strength-meter' . $suffix . '.js', array( 'jquery', 'password-strength-meter' ) );

                woocommerce_form_field("billing_country", array(
                    'type'              => 'country',
                    'class'             => array('form-row-wide'),
                    'label'             => 'Country',
                    'description'       => '',
                    'default'           => ''
                ), esc_attr( $_POST['billing_country'] ) );
            ?>

           <p class="form-row form-row-wide">
           		<label for="reg_billing_address_1" class=""><?php _e( 'Address', 'woocommerce' ); ?></label>
                <input type="text" class="input-text " name="billing_address_1" id="reg_billing_address_1" placeholder="Street address" value="<?php if ( ! empty( $_POST['billing_address_1'] ) ) echo esc_attr( $_POST['billing_address_1'] ); ?>">
           </p>

           <p class="form-row form-row-wide">
           		<input type="text" class="input-text " name="billing_address_2" id="reg_billing_address_2" placeholder="Apartment, suite, unit etc. (optional)" value="<?php if ( ! empty( $_POST['billing_address_2'] ) ) echo esc_attr( $_POST['billing_address_2'] ); ?>">
           </p>

           <p class="form-row form-row-wide">
           		<label for="reg_billing_city" class=""><?php _e( 'Town / City', 'woocommerce' ); ?></label>
                <input type="text" class="input-text " name="billing_city" id="reg_billing_city" value="<?php if ( ! empty( $_POST['billing_city'] ) ) echo esc_attr( $_POST['billing_city'] ); ?>">
           </p>

		   	<?php
                woocommerce_form_field("billing_state", array(
                    'type'              => 'state',
                    'class'             => array('form-row-first'),
                    'label'             => 'State / County',
                    'description'       => '',
                    'default'           => ''
                ), esc_attr( $_POST['billing_state'] ) );
            ?>

		   <p class="form-row form-row-last">
           		<label for="reg_billing_postcode" class=""><?php _e( 'Postcode / ZIP', 'woocommerce' ); ?></label>
                <input type="text" class="input-text " name="billing_postcode" id="reg_billing_postcode" value="<?php if ( ! empty( $_POST['billing_postcode'] ) ) echo esc_attr( $_POST['billing_postcode'] ); ?>">
           </p>

           <div class="clear"></div>	

           <br>

		   <p class="form-row form-row-wide">
           		<label for="reg_newsletter_opt_in" class=""><input type="checkbox" class="input-checkbox " name="newsletter_opt_in" id="reg_newsletter_opt_in" value="1" checked="checked"><?php _e( 'I would like to recieve the newsletter', 'woocommerce' ); ?>
				</label>
           </p>

This is working for displaying the fields but now I am struggling to identify how I add the validation and save functions?

I am not set on using either solution and would appreciate guidance on how best to accomplish this in my child theme. Thank you.

https://www.ads-software.com/plugins/woocommerce/