So for the playgrounds it says the runs end when talking to the shopkeeper for the last time, do you have to click through all the text before stopping the timer, or is it done once the text appears? Because I've seen people do both.

When you talk to the shopkeeper, the game gives you the track regardless of clicking through all the messages. If you log out with the dialog up, you'll still get the track

It's as soon as the text appears. Toontown is coded to reward almost everything before it actually appears done on the visible screen. When you defeat a flunky for a task, as an example, it is technically done as soon as the gag experience screen pops up. Example: Turning in Toontasks, defeating cogs, getting trolley beans, getting boss rewards, ect. So the final task is done as soon as the shopkeeper is talked to in technical terms.