If you are working with notebooks than see here regarding your connectivity issue.
Since that repo isn’t a template you can make a copy of, you instead have the option to fork it. And clone the fork locally. You can change the binder launch badge in the readme to point at your fork and push those changes to your fork.
You can work out the changes in the active session, download them to your local machine and then push back to your fork. Repeat that cycle. Here is a recent example of such a fork. Note that the badge point at that repo so that it launches with my cod changes.