How to update a file in remote repo, without cloning that repo first?

Impossible. But since a prospective commit would just need to have one single commit as its parent it's possible to employ the so-called "shallow cloning" and fetch just the tip commit of the branch you need. This will bring only a minimum amount of objects from the remote. Look for the --depth command-line option of git clone.

Yes you can push a new version using tagging

follow this steps

in your new project root

1. git init
2. git remote add origin [email protected]:yourusername/yourpoject
3. git tag -a v2.0 -m 'version 2.0'
4. git add .
5. git commit -m "New Version 2.0 :rocket:"
6. git push -u origin v2.0

now you have a new branch called v2.0 with your new project and your master branch stays untouched. After that if you wan't you can change your default branch in your github project settings.