how to refer to beginning/middle/end in Mandarin?
By "the beginning/middle/end", commonly Chinese words 初，开头，开始 /中，中间 /末，末尾，结尾 are related to them.


the beginning  /      middle     /end of the week (was hot) 
一周初，一周开始/ ? 一周中间(几天) /周末............In Chinese, there's not an commonly used expression for middle of a weekend. we don't say it much.
the beginning/middle/end of the book (was exciting) 
书的开头      /中间  /末尾，结尾
the beginning/middle/end of the summer (is when students arrive)
夏初  /仲夏   /夏末.......... “仲夏” is relatively literary. We don't say “夏中” much, personally I've never seen it before.
the beginning/middle/end of the year (seemed promising)
年初      /年中   /年末，年尾，年终..........As “年中” and “年终” share the same pronunciation &lt;niɑ̄n zhōng&gt;, make it clear if you use them in daily oral expression.
the beginning/middle/end of the speech (was inaudible)
演讲开始   /中间  /末尾，结尾
the beginning/middle/end of the word ....
as above
the beginning/middle/end of the movie
as above
the beginning/middle           /end of the hour
一小时开头     /半小时(eg. 3:30) / ？  .......We don't directly say "end of an hour" much in Chinese, but this: when you wanna say end of an hour like 4:50, just say “快5点” or “接近5点” or “将近5点”


Hope above helps. BTW, it may not be the same as your teacher told you, while I speak Mandarin of mainland China, there's few tiny differences of the language between Mainland and Taiwan, but feel free.