I did not download zen cart, and I did not upload them from my local computer.
Instead, I installed it directly onto my server as it was offered as an option in hosting website (fatcow.com). This automatically create a MySQL database and everything.

Now, I wonder if this type of installation will eliminate my options in customize the store. For example, how could I upload a template when I have no zen-cart folder on my local computer.

I can see the zen-cart folder in website's filemanager and have full control of domain and anything needed.