I installed wordpress on the server manually using filezilla. Now if i edit my wordpress website will it get automatically updated on my pc or do i need to download the changes manually? I want to have a backup of my website in case something goes wrong.
Wordpress will not update automatically until you do it. Whenever new version of wordpress is available , it will notify you in your wp admin panel and then you can update if you want.
You can update wordpress via filezilla by overwriting files only if you know which files need to update to get new version.
I suggest that always take backup of your site & database on some regular interval like weekly , daily whatever is suitable for you so in future if you face any issue in site then you can use recent backup.
For local files in your pc , you will have to compare code of files one by one with latest version files.
Here you can follow steps that How you can update wordpress via FTP : Update Wordpress via FTP