when you say “parked” are you switching your domain’s status in the panel between fully hosted and parked?
I think that makes sense with what you are describing. If that’s the case, then switch your domain to fully hosted, that’s the way it will have to be for you to upload files and be able to see them. You’ll obviously have to wait a bit for the changes to take effect, but then you should be good to go.
Now, as far as what your guests see while youre working on your layout and all is up to you. You can just create a index file that says “under construction” and put that in your web accessable area, and the visitors will see that instead of the list of files. There won’t be links on your index file so they won’t know about any of your other sutff. In the mean time you can be working in the “backgroud” and you’ll just view you rupdates by typing in the direct URL in your browser.
It will take search engines a while to crawl your site, so you don’t need to worry about people finding links and seeing your stuff for a couple weeks.
Alternativly you could set up a .htaccess for the domain so that you have to have a user name and password to access any of your site content, but then anyone trying to see your site will simply be greeted by a user name/password prompt, and nothing else. you can set up the htaccess in Panel > goodies > Htaccess.