SELECT 
  p.product_id, 
  ifnull(
    count(dp.post_id), 
    0
  ) as discussion_amount_posts 
FROM 
  cscart_discussion 
  INNER JOIN cscart_products as p ON (
    cscart_discussion.object_id = p.product_id
  ) 
  INNER JOIN cscart_discussion_posts as dp ON (
    cscart_discussion.thread_id = dp.thread_id 
    AND cscart_discussion.object_type = 'P'
  ) 
WHERE 
  dp.status = 'A' 
  and p.product_id in (
    317, 189, 501, 293, 78, 35, 234, 331, 484, 
    287, 292, 79
  ) 
GROUP BY 
  p.product_id

Query time 0.00083

JSON explain

{
  "query_block": {
    "select_id": 1,
    "table": {
      "table_name": "p",
      "access_type": "range",
      "possible_keys": ["PRIMARY"],
      "key": "PRIMARY",
      "key_length": "3",
      "used_key_parts": ["product_id"],
      "rows": 12,
      "filtered": 100,
      "attached_condition": "p.product_id in (317,189,501,293,78,35,234,331,484,287,292,79)",
      "using_index": true
    },
    "table": {
      "table_name": "cscart_discussion",
      "access_type": "ref",
      "possible_keys": ["PRIMARY", "object_id"],
      "key": "object_id",
      "key_length": "6",
      "used_key_parts": ["object_id", "object_type"],
      "ref": ["orbit_cscart_orbit_cscart.p.product_id", "const"],
      "rows": 1,
      "filtered": 100,
      "index_condition": "cscart_discussion.object_type = 'P'"
    },
    "table": {
      "table_name": "dp",
      "access_type": "ref",
      "possible_keys": ["thread_id", "thread_id_2"],
      "key": "thread_id_2",
      "key_length": "6",
      "used_key_parts": ["thread_id", "status"],
      "ref": ["orbit_cscart_orbit_cscart.cscart_discussion.thread_id", "const"],
      "rows": 7,
      "filtered": 100,
      "index_condition": "dp.`status` = 'A'"
    }
  }
}