"atrophy" - late 16th century: from French atrophier (verb), atrophie (noun), from late Latin atrophia, from Greek, ‘lack of food,’ from a- ‘without’ + trophē ‘food.’
Atrophy is also a medical term for when things waste away or get smaller. For example if a leg becomes paralysed the muscles will atrophy.
In short, yes. If you are really hard pressed to make a distinction τροφή is nourishment and φαγητό food. :)
Could say yes. "Τροφή" is more often used for the basic staff than "φαγητό". And is more formal word. E.g.: 1. Stuck in a virgin island: Έχουνε τροφή και νερό; (Do they have food and water?) 2. At home: Τι φαγητό έχουμε σήμερα; (What food do we have today?)