Have you paid for annual hosting? That's $9.95 or so per month (less for longer contracts) and will get you some server space for database and websites.
1) A parked page might show up on Google, but way down the search results since there's no content. You can set up your own Fully Hosted site and add a robots.txt to discourage search bots from indexing your site:
2) If your page is parked (via DreamHost Panel), you can't work on your site because it's not set up for hosting. Make your own parked page on a Fully Hosted domain if you want to work on your site or create something like a dev.example.com subdomain you can work on while example.com is Parked.