It sounds like you are about ready for local development but are just missing the db connection. To get that worked out you should use a copy of your live db, if you can export it from the live database you will import it locally into your MySQL. Once that is done you can then establish a connection to it from within DW. However, if you make any changes to the db you will need to export it from your local copy and import it into your live db to sync the records.
For the files you should copy all of the files from your web root into your local DW site root.
Are you trying to make any dynamic type of changes to the PowerStore? If not you could go without the db connection if you would just like to make design changes to the pages. In DW you could open up the pages and templates to alter the style and design, then upload to the live server when done.