Answers
How long do messaging apps keep your messages?
It varies enormously — from not at all, to until you delete them, to indefinitely. It is in the privacy policy, and it is the part most worth reading.
Some services store nothing on the server once delivered. Others keep everything so that a new device can sync history. Both are defensible and they have very different exposures.
Deletion also has degrees: removing a row from a live database is not the same as removing it from backups, and most policies mean the first.
Naven's privacy page states what is kept and for how long in specific terms rather than in general ones.