Developing On A Live Site
First, take backups of the templates, just incase! We store regular backups on the server too, but if you have a backup then you can be sure everything is ok.
If you're working locally then a best practice would be to put your template folder under version control, this way you could use a service (such as bitbucket which offers free private hosting) to store a remote backup of these files.
In Admin > Template manager, you can select the live template, but you can also select a "preview" template, only for your current logged in session, this means just for your session you can use a specific template folder, while every other user will see the current live one.
This now allows you to work over FTP, auto uploading changes, to a folder which only affects your session, not disturbing live sites.
As well as a session setting for the template, you can also set a specific different folder, just for mobile. So if you're working on migrating a site, but the main desktop site has alot of custom elements still to come in, or that simply dont work under the new responsive plan, then you can use this to make sure only mobile users get your new template.
In most cases it's best to provide a single responsive layout that's consistant, but we offer this just incase.