I once needed this and used this solution .

function flatten($array) {
    $return = array();
    array_walk_recursive($array, function($a) use (&$return) { $return[] = $a; });
    return $return;
}

This form works regardless of the number of sub-arrays you have and also independent of the keys. Ex: link

You can use the array_walk_recursive function:

array_walk_recursive($array, function ($item, $key) 
{
    global $Characeristics;
    if (! is_array( $item ) ) $Characeristics[] = $item;
});

$result = array( "Characeristics" => $Characeristics );

That is, if the value you are currently passing is not an array (it will be your feature string) is added to a new array.

Running the Idea

Example of how you can do it:

$arr = array(
    0 => array(1, 2, 3),
    1 => array(4, 5, 6)
);

$rs = array();
foreach ($arr as $v) {
    $rs = array_merge($rs, array_values($v));
}
unset($arr);

print_r($rs);

Be aware that this is an example. The original question array has one more level, but can solve with the same logic.

For your case it should look something like this:

$rs = array('Characteristics' => array()); // Esse array serve para guardar o resultado final

foreach ($arr['Characteristics']['external_area'] as $v) {
    //aqui mescla os valores
    $rs['Characteristics'] = array_merge($rs, array_values($v));
}
unset($arr); // Se não precisar mais desses dados, apague-os

print_r($rs);

Key names

If the name of the first key is unknown, you can get it with the key () function

$arr['a']['b'] = array();
echo key($arr['a']);
// retorna 'b'

For your specific case:

$arr['Characteristics']['external_area'] = array();
echo key($arr['Characteristics']);
// retorna 'external_area'

Implementing in Sample Code

$rs = array('Characteristics' => array()); // Esse array serve para guardar o resultado final

$k = key($arr['Characteristics']); // obtém o nome da primeira chave

foreach ($arr['Characteristics'][$k] as $v) {
    //aqui mescla os valores
    $rs['Characteristics'] = array_merge($rs, array_values($v));
}
unset($arr); // Se não precisar mais desses dados, apague-os

print_r($rs);

I developed a function that runs through the array and merges the array, take a look, I considered the array $characteristics as the first one you posted in the question, I hope it helps

var_dump(getAllCharacteristics($characteristics));
die;

function getAllCharacteristics($characteristics) {
    $newArray = [];
    foreach ($characteristics as $characteristic) {
        if (is_array($characteristic)) {
            $newArray = array_merge($newArray, getAllCharacteristics($characteristic));
        } else {
            $newArray[] = $characteristic;
        }
    }
    return $newArray;
}

The output of the var_dump function would be:

array(9) {
  [0]=>
  string(7) "varanda"
  [1]=>
  string(10) "lavanderia"
  [2]=>
  string(7) "piscina"
  [3]=>
  string(5) "muros"
  [4]=>
  string(13) "area_serviço"
  [5]=>
  string(9) "piso_frio"
  [6]=>
  string(9) "alvenaria"
  [7]=>
  string(12) "azulejo_teto"
  [8]=>
  string(13) "massa_corrida"
}