If I use the demo - decide I like it and then go ahead and purchase - can I keep what I have done or do I need to start over.

Well, the demo is actually a fully working store, that is yours to keep.

Here's the catch:

Only IF you want to remove the copyright at the bottom, then you are required to purchase a license. This helps support the developers in improving the product in the future. You also get dedicated technical support (Otherwise, you need to rely on these forums, which in the majority of cases will answer your queries very well).

So, you either keep your existing "demo" store, or buy a license for copyright removal/support.

There's no need to re-install, whether you license your store or not.

... and copyright on the top of the browser ( Powered by CubeCart )

To make it full version in the ACP, just insert the activation code in there and magic, you have a registered version