As I have written in your post at StackOverflow board:
Please look at Upload localhost changes to live server
If you are only making file changes, you should copy the live site and set it up on a local wordpress server. On the local wordpress server, just edit the theme as you like, and when you made your changes. Upload only the theme to your live site.
If you are also making database changes, please read the link in the top of my answer.
Remember to make backup, always make backup, backup is 1. priority in every case. If you screw up, make sure to get back online as fast as possible.
You can use a plugin as ‘Duplicator’ https://wordpress.org/plugins/duplicator/ to copy your live wordpress installation.