11. His sister-in-law’s letter came as a surprise to Chuck.
The compund noun is not separated. The 's 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 's 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 's 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". Whose 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 's. 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 Smith's or Smiths's, 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 's goes at the end of the last name.