V13 doubt, what about the updates

is it necessary to upgrade to version 14, or we can simply use version 13?
will the updates and fixes provided by erpnext for version 13 after 31 dec or not?

There will be no bug fixes after 31st Dec. So if you want to continue to receive fixes/features etc you should update. In general, it’s a bad idea to continue using EOL software, unless it’s on airgapped machine or something.

Generally Software updates are painfull rule of thumb is If you have bug look for later versions if it is solved or not if yes move to new one. exception is security updates!! otherwise if life is chill you wake up eat banana and holy molly stuff. don’t touch it