Betty,
Here are my answers
Uploading my theme file:
First you must install the WP files to your host. You can do this through CPanel on HostGator. Here is a step-by-step post to do that:
http://www.shoutmeloud.com/how-to-in...hostgator.html. For added security, your admin name should be something unique and not just admin.
Once set up you then log into your WP dashboard which you can access at mysite.com/wp-admin (add the /wp-admin after your domain name) and log into your site.
Once you are logged in then you can upload and activate your chosen theme there. There are tons of tutorials on the web so you should have no problem finding a good resource.
Home Page:
Once your site is active yes it is live. To work on your site before making live you can add a subdomain to your site, install WP and theme and then work on it there. For example betasite.mysite.com. Once you are comfortable with the look and feel then you simply move your files over to your root directory.
This method will allow you to have your old site live while working on your new site.
When you are ready to go live then you can just move to the root, instructions here:
http://codex.wordpress.org/Moving_WordPress
It sounds heftier than it is and I would suggest that you educate yourself first on the processes. Also remember to back-up all files before moving your new site.