Learn German: Sie bekommt die Haare glatt geföhnt. - She is getting her hair blow-dried straight.

In an active sentence, this would be "Jemand föhnt ihr die Haare" (Someone blow-dries her hair), where ihr is the dative recipient of the action. The recipient passive (or dative passive) allows you to make that dative recipient the subject of the sentence. So ihr becomes Sie, and you use a conjugated form of bekommen plus the past participle (geföhnt) to express that the action is being done for her. It works almost exactly like the English "getting [something] done."

Why does the sentence use die Haare instead of ihre Haare?

In German, when an action is performed on body parts or items of clothing, you usually use the definite article (die) instead of a possessive pronoun (ihre) as long as the "owner" is already obvious from the context. Since Sie is the subject receiving the action, it is perfectly clear whose hair is being dried.

Why is the word glatt (straight) placed right before the past participle?

glatt functions here as a resultative adjective—it describes the intended result of the action (she is getting it blow-dried so that it becomes straight). In German, adjectives that describe the result of an action are usually placed right before the verb or past participle at the end of the clause.

Is the verb föhnen related to the weather term der Föhn?