"the price for an item is too high" - not a noun phrase. Actually, this is a clause, as it has a predicate of its own.
"a bottle of water while strolling" - not a noun phrase. "A bottle of water" would be a noun phrase (a phrase that has a noun as a headword), but "while strolling" is an adverbial phrase that describes the verb "buy".
"The same brand of bottled water" - noun phrase. The headword is "brand", and all the other words cling to it and provide additional explanation.
"a pair of athletic shoes" - noun phrase. The headword is "pair".
It is good idea. some students will not pay attention to the teacher if they have phone on them , of course they will keep playing on their phone while the teacher is teaching , and what if their phones got lost? the school will get attacked by the parents for not being careful
This would be "in media res" meaning "in the middle of things." It begins, quite frankly, in the middle of things and carries on from there.