Do I need to save my spreadsheet after editing in Zoho Sheet?

Do I need to save my spreadsheet after editing in Zoho Sheet?

No. Every modification you and your collaborators make to the Zoho Sheet spreadsheet will be automatically saved. The last modified time of the spreadsheet is shown at the right top corner. 

You can use features like Audit Trail and Version History to take a look at the changes made to your spreadsheet and access different chronological versions of the spreadsheet.