None of the situations listed are appropriate for using informal language.
The situation in which it is appropriate to write using informal language is: a postcard to a friend.
The appropriate situation to write using informal language is for a postcard to a friend. When you're writing to a friend, it's typical to use a more casual tone and language choice. However, for other situations like a cover letter for a job application, a legal document to present in court, or a scientific research article, it's important to use formal language as these contexts require a professional and objective tone.