I suspect this is built in and the cart contents are stored in a cookie. So providing the user has cookie enabled it should work.
As to incorporating the shopping cart into existing pages depends on how much work you want to do and what your knowledge of CSS and Dreamweaver is.
PS3 is template based so you could modify the template with your existing design and that would apply to your site.
I think my prefered method would be to take take the exisiting design and save it as a template. I'd then cut and paste all the WA code from the supplied shop template into my new template (if you follow).
Once I was happy I'd then save my new template over the WA template and that would of course update the whole site.
Might be a lot of work but if you are confident I do not forsee any real problems.
What I would say is make sure it all functions before you start and take lots of backups
No doubt technical will come back to you but to me it's all possible.