Is it now possible to spy on other person’s iPhone using microphone?

There is this app on the Appstore “Find My Kid” and “Chat with parents”. They allow to the first app to start listening to microphone of the second app even without notification. Even when the app is in the background and the screen is off. So I have two questions. How could Apple allow such an app? And how technically? If it’s background modes, then which one?

Number of ways of distributing 6 objects to 6 persons

I had some doubt regarding below problem.

The number of ways of distributing 6 objects to 6 persons such that at least one of them does not get anything.

I worked like

Without restriction total ways= $ 7^6$

Number of cases in which all persons get something=$ 6!$

Number of cases where at least one person does not get anything=$ 7^6-6!$

Am I correct?

Also if the probability is asked for at least one person don’t get any object then should it be equal to $ \frac{7^6-6!}{7^6}$ ?

Progress visualization of a person’s self-development?

I’m talking about any kind of self-improvement that is monitored/tracked. Most common example are fitness trackers or apps.

Now are there any guidelines or examples on this?
How would one best visualize the progress of the user over time, so that it will help him/her reflect upon it?


Context

In my specific case it’s about mental improvement (self-affirmation, confidence exercises and stuff like that). So participants have a main goal and finish certain steps on the way towards it.
The data I’ll have will most likely be number of finished steps, distance to reaching the goal, self-reflection entries and possibly other ways.

The process is supposed to happen over approx. 3 weeks, with the user finishing a “step” approx. every 2-3 days and getting a new one then.

Since self-reflection is a crucial part of such a mental improvement process (Paper1 & Paper2) I really want to present the data in the most helpful way possible.