Plural possessive is the answer
It's an adverb phrase of time,
We stopped. When? After the game
Okay. I cannot see the article, again but will try my hardest to answer this anyway.
The purpose can usually be seen in the first sentence or paragraph (unless you have an excerpt). Though it may not be too specific it will usually be backed up by evidence later in the passage. A purpose can always be proven by text details.
Choice of details: should support the purpose
organization: Some things are good for some purposes.
e.g. cause effect, shows the good or bad effects of a purpose. The author can support the purpose or no.
chronological can show how something has changed over time.
etc.
Try to identify the main structure and how the passage is organized and how it supports the main idea.
