Do I need to save my work?

No. Docs and Spreadsheets save automatically while you work. The cloud icon at the top shows Saved with the time

If the connection drops:

• Docs: keep writing. Changes are kept on your device and sync when you are back online
• Spreadsheets: keep the tab open. Your edits are sent when you reconnect. If someone else changed the spreadsheet in the meantime, you are asked to redo your offline edits

Every save also goes into Version history, so you can always go back