Drupal 'add more' and 'remove single' AJAX buttons on multi value custom field using FormAPI

mymodule.css

input.form-submit.button-small {
  padding: 4px 8px;
  font-weight: bold;
}

.container-inline input.form-submit.button-small + .ajax-progress.ajax-progress-throbber .throbber {
  position: absolute;
  left: 19px;
  margin-top: 7px;
}

.container-inline input.form-submit.button-small + .ajax-progress.ajax-progress-throbber .message {
  display: none;
}

mymodule.module

function mymodule_ajax_example_add_more($form, &$form_state) {
  $form['field_container'] = [
    '#type' => 'container',
    '#weight' => 80,
    '#tree' => TRUE,
    // Set up the wrapper so that AJAX will be able to replace the fieldset.
    '#prefix' => '<div id="js-ajax-elements-wrapper">',
    '#suffix' => '</div>',
  ];

  $form_state['field_deltas'] = isset($form_state['field_deltas']) ? $form_state['field_deltas'] : range(0, 3);

  $field_count = $form_state['field_deltas'];

  foreach ($field_count as $delta) {
    $form['field_container'][$delta] = [
      '#type' => 'container',
      '#attributes' => [
        'class' => ['container-inline'],
      ],
      '#tree' => TRUE,
    ];

    $form['field_container'][$delta]['field1'] = [
      '#type' => 'textfield',
      '#title' => t('Field 1 - ' . $delta),
      '#size' => 10,
    ];

    $form['field_container'][$delta]['field2'] = [
      '#type' => 'textfield',
      '#title' => t('Field 2 - ' . $delta),
      '#size' => 10,
    ];

    $form['field_container'][$delta]['remove_name'] = [
      '#type' => 'submit',
      '#value' => t('-'),
      '#submit' => ['mymodule_ajax_example_add_more_remove'],
      // See the examples in ajax_example.module for more details on the
      // properties of #ajax.
      '#ajax' => [
        'callback' => 'mymodule_ajax_example_add_more_remove_callback',
        'wrapper' => 'js-ajax-elements-wrapper',
      ],
      '#weight' => -50,
      '#attributes' => [
        'class' => ['button-small'],
      ],
      '#name' => 'remove_name_' . $delta,
    ];
  }

  $form['field_container']['add_name'] = [
    '#type' => 'submit',
    '#value' => t('Add one more'),
    '#submit' => ['mymodule_ajax_example_add_more_add_one'],
    // See the examples in ajax_example.module for more details on the
    // properties of #ajax.
    '#ajax' => [
      'callback' => 'mymodule_ajax_example_add_more_add_one_callback',
      'wrapper' => 'js-ajax-elements-wrapper',
    ],
    '#weight' => 100,
  ];

  $form['other_field'] = [
    '#type' => 'textfield',
    '#title' => t('Other field'),
  ];

  return $form;
}

function mymodule_ajax_example_add_more_remove($form, &$form_state) {
  $delta_remove = $form_state['triggering_element']['#parents'][1];
  $k = array_search($delta_remove, $form_state['field_deltas']);
  unset($form_state['field_deltas'][$k]);

  $form_state['rebuild'] = TRUE;
  drupal_get_messages();
}

function mymodule_ajax_example_add_more_remove_callback($form, &$form_state) {
  return $form['field_container'];
}

function mymodule_ajax_example_add_more_add_one($form, &$form_state) {
  $form_state['field_deltas'][] = count($form_state['field_deltas']) > 0 ? max($form_state['field_deltas']) + 1 : 0;
  
  $form_state['rebuild'] = TRUE;
  drupal_get_messages();
}

function mymodule_ajax_example_add_more_add_one_callback($form, $form_state) {
  return $form['field_container'];
}

How to manage this on Edit form ?

THANK YOU! Woo! ;-)

Here is a D8 version if anyone is interested:

<?php
/**
 * @file
 * Contains \Drupal\mymodule\Form\FormTest.
 */
namespace Drupal\mymodule\Form;

use Drupal\Core\Form\FormBase;
use Drupal\Core\Form\FormStateInterface;

class FormTest extends FormBase {
  
  /**
   * {@inheritdoc}
   */
  public function getFormId() {
    return 'mymodule_form_test';
  }
  
  /**
   * {@inheritdoc}
   */
  public function buildForm(array $form, FormStateInterface $form_state, $item_id = NULL) {
  
    // Disable caching for the form
    $form['#cache'] = ['max-age' => 0];
    
    // Do not flatten nested form fields
    $form['#tree'] = TRUE;
    
    $form['field_container'] = array(
      '#type' => 'container',
      '#weight' => 80,
      '#tree' => TRUE,
      // Set up the wrapper so that AJAX will be able to replace the fieldset.
      '#prefix' => '<div id="js-ajax-elements-wrapper">',
      '#suffix' => '</div>',
    );
    
    if ($form_state->get('field_deltas') == '') {
      $form_state->set('field_deltas', range(0, 3));
    }
    
    $field_count = $form_state->get('field_deltas');
  
    foreach ($field_count as $delta) {
      $form['field_container'][$delta] = array(
        '#type' => 'container',
        '#attributes' => array(
          'class' => array('container-inline'),
        ),
        '#tree' => TRUE,
      );
    
      $form['field_container'][$delta]['field1'] = array(
        '#type' => 'textfield',
        '#title' => t('Field 1 - ' . $delta),
        '#size' => 10,
      );
    
      $form['field_container'][$delta]['field2'] = array(
        '#type' => 'textfield',
        '#title' => t('Field 2 - ' . $delta),
        '#size' => 10,
      );
    
      $form['field_container'][$delta]['remove_name'] = array(
        '#type' => 'submit',
        '#value' => t('-'),
        '#submit' => array('::mymoduleAjaxExampleAddMoreRemove'),
        '#ajax' => array(
          'callback' => '::mymoduleAjaxExampleAddMoreRemoveCallback',
          'wrapper' => 'js-ajax-elements-wrapper',
        ),
        '#weight' => -50,
        '#attributes' => array(
          'class' => array('button-small'),
        ),
        '#name' => 'remove_name_' . $delta,
      );
    }
  
    $form['field_container']['add_name'] = array(
      '#type' => 'submit',
      '#value' => t('Add one more'),
      '#submit' => array('::mymoduleAjaxExampleAddMoreAddOne'),
      '#ajax' => array(
        'callback' => '::mymoduleAjaxExampleAddMoreAddOneCallback',
        'wrapper' => 'js-ajax-elements-wrapper',
      ),
      '#weight' => 100,
    );
  
    $form['other_field'] = array(
      '#type' => 'textfield',
      '#title' => t('Other field'),
    );

    return $form;
  }
  
  /**
   * @param array $form
   * @param \Drupal\Core\Form\FormStateInterface $form_state
   */
  function mymoduleAjaxExampleAddMoreRemove(array &$form, FormStateInterface $form_state) {
    // Get the triggering item
    $delta_remove = $form_state->getTriggeringElement()['#parents'][1];
    
    // Store our form state
    $field_deltas_array = $form_state->get('field_deltas');
    
    // Find the key of the item we need to remove
    $key_to_remove = array_search($delta_remove, $field_deltas_array);
    
    // Remove our triggered element
    unset($field_deltas_array[$key_to_remove]);
    
    // Rebuild the field deltas values
    $form_state->set('field_deltas', $field_deltas_array);
    
    // Rebuild the form
    $form_state->setRebuild();
    
    // Return any messages set
    drupal_get_messages();
  }
  
  /**
   * @param array $form
   * @param \Drupal\Core\Form\FormStateInterface $form_state
   *
   * @return mixed
   */
  function mymoduleAjaxExampleAddMoreRemoveCallback(array &$form, FormStateInterface $form_state) {
    return $form['field_container'];
  }
  
  /**
   * @param array $form
   * @param \Drupal\Core\Form\FormStateInterface $form_state
   */
  function mymoduleAjaxExampleAddMoreAddOne(array &$form, FormStateInterface $form_state) {
  
    // Store our form state
    $field_deltas_array = $form_state->get('field_deltas');
    
    // check to see if there is more than one item in our array
    if (count($field_deltas_array) > 0) {
      // Add a new element to our array and set it to our highest value plus one
      $field_deltas_array[] = max($field_deltas_array) + 1;
    }
    else {
      // Set the new array element to 0
      $field_deltas_array[] = 0;
    }
  
    // Rebuild the field deltas values
    $form_state->set('field_deltas', $field_deltas_array);
  
    // Rebuild the form
    $form_state->setRebuild();
  
    // Return any messages set
    drupal_get_messages();
  }
  
  /**
   * @param array $form
   * @param \Drupal\Core\Form\FormStateInterface $form_state
   *
   * @return mixed
   */
  function mymoduleAjaxExampleAddMoreAddOneCallback(array &$form, FormStateInterface $form_state) {
    return $form['field_container'];
  }
  
  /**
   * {@inheritdoc}
   */
  public function submitForm(array &$form, FormStateInterface $form_state) {
    // Submit Form
  }
  
}

Thank you, this was exactly what I needed to figure out dynamic forms in Drupal 8.

Thank you Alex and Mitchell, you make my day !

Thank you, Alex and Mitchell, you really helped me a lot.