For example: When I set up a new facebook account for my mother (at her explicit wish), she had no friends or interests marked yet. Facebook showed her some random ads and posts.
During the setup I was scrolling through her timeline and my phone beeped so I stopped scrolling for about 2 seconds. The post shown was a random post about some fish.
When I picked it up, I saw it quickly replacing the next random post with something about the same kind of fish. So evidently it even looks at how long you look at certain content to determine your interests.
I suppose it is possible to derive other algorithmic determinations using similar methods.
It does. Instagram constantly sends back telemetry including your scroll position, which can then be used to determine what you were looking at and for how long. Scroll right past an ad? you probably won't see it again; the algorithm knows it didn't have an impact on you. Meanwhile, spend a few seconds reading what it says, and this teaches the algorithm that you are interested in similar content.
"What can be asserted without evidence can also be dismissed without evidence."
The same cannot be said for phone apps.
But about your first point. I don't think even the designers and maintainers of this blackbox understand the system. Looking at it from that point of view, the chances of a hacker finding proof for this is pretty low.
It would be pretty easy to show that a) sound is not being continually recorded and streamed over the internet and b) the device is not using enough processing power to decode speech. Both have been done, so this is veering into conspiracy theory territory.
There's actually nothing hard about the concept of a mobile phone, it's just a computer (or could even be a simple PCB) with a mic and speaker. No need for "secret sauce" standards such that nobody can tell if it's secure (I mean it isn't, the bugs just get patched every week, day, nanosecond, whatever). Hell, you can even make a completely open and simple (even more important than open) phone communication standard and charge 1 billion people tens of dollars per month to use your network and become the richest person on earth.
edit: I mean facebook, or whatever (also facebook would have to gain access to the mic [maybe facebook has mic permission i guess, i am unfamiliar with smart phones])
Facebook has access to your mic if you ever use it for its voice com functions (do not do that) and do not explicitly remove the permissions to access teh mic (do do that).
They have been caught several times. Thing is people give them permission to record through the mic so it is legal.
Do not confuse legal with good, it is evil.
Then randomly assign the products from the first step to the volunteers, give them information about the product on paper and ask them to hold verbal conversations about such such products.
If they start getting adverts that happen to match the subject of those verbal conversations, something is going on.
Sometimes you never do find out what happened.
So, one meta-step up in abstraction? People "notice" these these things which they talk about and now you're especially sensitive to hearing them?
