I wonder what device for knocking a ball around on a smooth, flat surface would sit comfortably in the very handy notch cut out for it right where you are looking for a plunger?

Yes, indeed: a cue stick!

Cigarette-smoking kids from a Lewis Hine photo!

I don't get it. The middle table has no pockets. What type of game can be played on such a table?

[Billiards. - Dave]

Many thanks for the enlargement, Dave. Now you've had me spend an enjoyable afternoon planning a possible reproduction of this great-looking piece. Cheers, mate!

There is no spring loaded handle to propel the ball forward. I can only conclude that the ball was drawn back onto a spring. How many points for ringing the bell in the centre? Magic picture. As one who spent his entire youth playing Bally's machines, eg Bally Beauty, County Fair, and Carnival Queen, this is a portent of things to come.

That great early pinball/bagatelle table at the end of the room is prompting at least two of the seven deadlies in me right now.

[Click to enlarge.]

Yes, we got Trouble, that starts with "T," which rhymes with "P," and that stands for Pool!