ElasticSearch filter results by multiple ORs not working

[CutThis]

I'm trying to query results similar to (totally new with ES):

$query = 'select * from promoter where (id_assigned_topic = ' . $id_topic . ' or id_topic_father = ' . $id_topic . ' or id_topic_grandfather = ' . $id_topic . ') and lower(name) like "%' . $search . '%" order by ranking DESC LIMIT ' . $limit_low . ',' . ($limit_high - $limit_low) . ';';

and I have built this search query for ElasticSearch:

$params = [
            'index' => 'es_promoters',
            'type' => 'data',
            'from' => $limit_low, 
            'size' => ($limit_high - $limit_low),
            'body' => [



                  "query"=> [
                    "bool"=> [
                      "must"=>[
                                "query_string" =>   [
                                                        "fields" => ["name"],
                                                        "query" =>  $search 
                                                    ],
                                "query_string" =>   [
                                                        "fields" => ["name"],
                                                        "query" => '"' . $search . '"'
                                                    ],
                                "query_string" =>   [
                                                        "fields" => ["name"],
                                                        "query" => '*' . $search . '*'
                                                    ],

                                ],
                                 "filter" =>[
                                        "bool" => [
                                                 "should" => [ 
                                                             "term" => [ "id_assigned_topic" => $id_topic ],
                                                             "term" => [ "id_topic_father" => $id_topic ],
                                                             "term" => [ "id_topic_grandfather" => $id_topic ],
                                                            ],
                                                "minimum_should_match" => 1
                                                ]
                                            ]



                            ]
                          ],



                ]
            ];

If I remove everything from the "filter" part I get all the results to match the names, however I cannot do an OR between the topic_ids.

my questions would be:

how can I do an OR between the various topic_ids?
how do I sort the final results descending by ranking?