How to load custom block via code?

Place the block in the disabled section at admin/structure/block, this creates a block instance with your block_content type, give it a nice easy to remember machine name.

By placing it in the disabled section, it won't show up, until you load it programatically.

Then using your machine name:

$machine_name = 'myblock';

$block = \Drupal
  ->entityTypeManager()
  ->getStorage('block')
  ->load($machine_name);
if (!empty($block)) {
  $block_content = \Drupal::entityTypeManager()
    ->getViewBuilder('block')
    ->view($block);

  $pre_render = $block_content;
}

If you really want to get the rendered fields, you can do:

$render = \Drupal::entityTypeManager()
  ->getViewBuilder('block')
  ->build($pre_render);

But it is more standard practice to use Drupal's formatters and such and perhaps a custom template, rather than building the block and extracting elements from the rendered render array.

There are two questions. How to load and render a configured block is answered perfectly by @oknate.

The second question: More than that how to get values of these block fields 'x' and 'y' by loading the block?

That's easy, because you've already loaded the block content entity, where the fields are stored in the database.

$block = \Drupal\block_content\Entity\BlockContent::load($bid);

You can access the value from the text field

$text = $block->field_y->value;

and get the url from the image field.

$image_url = file_create_url($block->field_x->entity->uri->value);

Try this code, include EntityInterface

   // Block 
   use Drupal\Core\Entity\EntityInterface;

// the last part of the parameter is the block id

  $block = \Drupal\block\Entity\Block::load('yourblockid');
  $block_content = \Drupal::entityManager()
    ->getViewBuilder('block')
    ->view($block);
  drupal_render($block_content);

My case was different: I am loading a custom block in the .theme file. I was not able to get the exact "Block ID" in a digit.

I got the block machine name. In this case, use the following code.

$block_config = \Drupal\block\Entity\Block::load($machine_blockid);
$uuid = $block_config->getPlugin()->getDerivativeId();
$block_content = \Drupal::service('entity.repository')->loadEntityByUuid('block_content', $uuid);
if ($block_content) {
  $img = file_create_url($block_content->field_X_image->entity->uri->value);
  $color = $block_content->field_Y_textfield->value;
}

Otherwise, use the following code. $bid is the block content id. You see this in /block/[bid].

$block = \Drupal\block_content\Entity\BlockContent::load($bid);
$x_img_url = file_create_url($block_content->field_X_image->entity->uri->value);;
$y_textfield_value = $block_content->field_Y_textfield->value;