How can I start a new document without loosing the content of the rapid memories?
Besides of the rapid memories you have the option to save your texts in iTunes File Sharing or in various cloud services.
Just open the menu on the bottom left and tap on "save as ..." and choose a destination for your text. Now you may give your text a file name and save it. Beware: After saving the document you are in the new document and not in the origin rapid memory. To start a new document in the rapid memory, tap on the rapid memory you were working in before and tap on the bin to delete the text. The app will ask you if you really want to delete the text in the current rapid memory. Since you saved your text in your local storage or cloud, you can delete the text from the rapid memory and start a new text.
If you don't go back to the rapid memory after saving the text and you tap on the delete button, the app will ask you if you want to delete the text or remove the file. If you choose "delete text", the text will be deleted in the saved document and the file is still in your folder (without text in it). If you choose "remove file", the file will be removed from the folder completely.