Learn English – Meaning of “I’m surprised you ever do that.”

"off the top" in general and here means the first 5 hours

In "off the top of my head" it means the first idea that came into my mind. Similar principle

The word affinity is a synonym or euphemism for mistress. The passage is quoting a proverb making the rounds at that time. Notice that this passage uses quotation marks to indicate words which are a direct quotation. See for example, the Coshocton Tribune, June 3, 1918, p. 4:

A married man with an affinity always runs the risk of talking in his sleep [emphasis added].

The example above is clearly referring to a marital indiscretion, but the specific form it takes is not identified in the quoted proverb. It might refer to simple adultery, or to another taboo such as homosexuality, or to any form of infidelity in general.

@KitFox found another newspaper proverb in The Mt. Sterling Advocate, December 28, 1922. This one makes clear that affinity was used at the time to mean mistress:

The rule that a man’s affinity is younger and better looking than his wife is one that knows blamed few exceptions [emphasis added].