It is best to upload the files to your server first and go through the install. Then you can edit the files for the store back in DW.
Unless you have remote access to the MySQL server you will need to have the database locally to do more development. To move the db from the live server you will need to export it from the live server, then import it locally. After you have done that you will need to login and update some values in the wa_settings table. In here you will want to update the Root URL as well as the local and remote roots. This will allow you to have a copy of the db locally so that you can modify the pages and server behaviors in DW.
As for using other extensions on PowerStore it is a standard php and html site so you should be able to use any of your current extensions on the PowerStore. The store is designed to work properly in it's default state and it is not suggested to try and update it unless you are very comfortable with the types of edits you are making. Before you make any edits you should make sure to backup the site so that you can revert it if there are any problems.