Yes Hanoi is ok with 500 k seasoned for a month. Important to ensure the school is aware of the docs to give you for approval. Good idea to check the threads to see if anyone else has been approved with that school.
Does the cooking course have a record of DTV approvals? I think Laos still requires 3 months seasoning of the 500k. Hanoi would be quicker. 9 months could be viewed more favourably than 6 mths.
11 business days is the approval term in Cambodia. Best to stay in Cambodia until approved incase of being asked to attend an interview or provide further proof of stay in Cambodia.