Different publishers are likely to handle the punctuation differently. I doubt that you'll be able to please them all, whichever convention you adopt.
At this point, I'll express my own preferences plus my reasons for those preferences.
Where you wrote
"We can't know for sure," he mused, leaning back in his chair, "Not until we ask more questions."
I would turn the dialogue into two separate sentences:
"We can't know for sure," he mused, leaning back in his chair. "Not until we ask more questions."
This is particularly justified here, because if you cut out the description and present the dialogue on its own,
"We can't know for sure, not until we ask more questions."
it becomes apparent that what you wrote is a run-on sentence (i.e. its clauses are grammatically entirely independent).
With your other query sentence,
I have to get out of here, he thought, But there's not enough time.
the interior monologue is not a run-on:
I have to get out of here, but there's not enough time.
Accordingly, I would put but in lower case:
I have to get out of here, he thought, but there's not enough time.
In that sentence, you don't need to capitalize but to signal the resumption of the monologue: the italics are already doing that.
You capitalize titles when they are referring to a specific role in a specific organization, or a person that fills that specific role. This follows the basic principles for proper nouns: Mr. Rogers, Mrs. Doubtfire, Dr. Phil. For example, a chief executive officer leads a company, but Chief Executive Officer Mark Zuckerberg runs Facebook.
So, all of your examples are correct: you're referring to a specific role at a specific company. If you were writing about hiring managers in general, it wouldn't be capitalized.
As for your long example:
Just recently I met Mr. Adams (previously Managing Director and Finance Director...
You might use a shorter word, like "formerly" or something, but I don't think you can make it too much shorter, given the length of the title.
Best Answer
Unless "city" is part of the name (i.e. "Carson City" or "New York City"), it's not capitalized after the city's name. Even used before (as in "City of"), the capitalization only happens if the title of the city in question actually has that name ("City of London", "City of New York").