You can open a second or third instance of material files via the three dots menu. You then have the app multiple times open and can copy/cut and paste between them.
Its not quite two panes but maybe better on a small screen. Its also a feature that’s easy to miss.
Probably nothing bad happens with those faxes. A malicous actor would still need access to the physical analogue line or to the network to sniff the RTP packets (depending on how the fax is transmitted) on one of the two sides. In theory all providers involved could also sniff the traffic since calls/faxes are never end to end encrypted. But something could happen, and I dislike it very much that they demand their users to take this risk.