What happens to tasks I did not finish?

Tasks you typed in the room belong to that session. When it ends they are done with - they do not pile up on your Tasks page. The recap lists the ones you did not finish, each with a Keep in My tasks button (and one Keep all button above them): tap it and that task joins My tasks. Tasks that were already in My tasks or copied from Recurring are shown quietly at the bottom as already on your lists - they are safe. If you just leave, nothing is asked and nothing is lost that mattered: the session keeps its own history.