These are off the top of my head and really, they are only guesses :S
I guess this is more to get you thinking rather than giving you a clear-cut answer.
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When you describe the context, you describe what's happening at that time "Cooking a fish in a kitchen being broadcasted"
When you describe the domain, you tend to be more general and just use one or two words "Cooking" or "Television Cooking"
With the field, to me it sounds more academic, so maybe the words you use to describe the field could be a topic in a textbook "
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Metonymy and Synecdoche, no clue maybe one is to do with only nouns whilst the other is to do with nouns&verbs?
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Repetition is more to do with words whilst parallelism is more to do with sentences
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Overstatement sounds less technical, you can use it in a general conversation. And it might also be more negative than hyperbole - Situation where two people are gossiping "Man, thats such an overstatement"
You know another word that goes with these two is 'exaggeration'