> Not without money or equivalent trade involved.

This isn’t generally true. The copyright holder need only claim that the value of their copyrighted work or the profits received by its distribution has been reduced or lost. I’m not sure they even need to make such a claim, as courts have already determined that commerciality isn’t a requirement for infringement. It’s a matter of unauthorized use, distribution or reproduction, not trade.

They of course will likely never know and might not bother to litigate given the private and uncommercial nature, but they still have the right to do so.

They would weigh the financial and reputational cost of litigating against children sharing images and decide not to. Of course if one had 10000 friends and provided this service to them in a visible manner, then they’d probably come knocking.

IANAL, but my understanding is that it's more complicated than this. Generally commercial benefits (i.e. taking money) is one of the aspects being taken into consideration to decide if something is fair use, but it's not the only one and not making a monetary/commercial benefit does not guarantee that work is considered fair use (which is the exception we're talking about here).

Not true. There were many cease and desist orders for fanfiction, which was intended as open source.