11. His sister-in-law’s letter came as a surprise to Chuck. 
The compund noun is not separated. The <em>'s</em> is added to the end of the noun.
12. Arizona’s climate is dry. 
The possessive of a singular noun is formed by adding an <em>'s</em> to it.
13. She is writing a paper on Byron’s and Shelley’s poems. 
Since the poems belong to two separate people--they did not compose them together, so this is not shared ownership--the <em>'s</em> goes after each of their names. 
14. I met a man whose sister I know. 
Who's is a contraction meaning "who + is", expressing "what or which person or people". <em>Whose</em> is a possessive pronoun. 
15. It’s too bad that the dog’s foot got hurt. 
This is the same case as number 12.
16. Smith’s house is red. 
If a singular noun ends in s, the rule is to also add <em>'s</em>. The only time a noun ending in s will only have an apostrophe added is when is plural. So in this case it could only be<em> Smith's</em> or <em>Smiths's, </em>depending on the name, since it's not a plural noun.
17. Kevin and Mike’s parents, Arthur and Alice Brooks, are both scientists.
Kevin and Mike share the same parents. As this is a shared possessive, the <em>'s</em> goes at the end of the last name.