I understand when I put my app on, it will run on RStudio Server (right?).
For who my R code and input data is available ? is a domain I don't know anything about (and it appears to be on sale for only $2,500!)

But is a nice tool for deploying your Shiny applications on the Web.
Note under the security section, it says Each Shiny application runs in its own protected environment and access is always SSL encrypted. Standard and Professional plans offer user authentication, preventing anonymous visitors from being able to access your applications.

I think answers to your questions are in the documentation: