Hi Carlos
Answering the questions :
1) Publish the site to BC and then create a form on BC end , assign to a secure zone ( which you will have to create ).
2) You can register users in your site using same form.
3) Use login form in page where user can login , landing page for secure zone can be made as web app page. Web app needs to be created for customer accounts and in layout you can use different tags to show cases information which user has submitted etc.
4) Web app is the way out.
http://helpx.adobe.com/business-catalyst/partner/add-secure-area-your-site.html
http://www.bcgurus.com/tutorials/how-to-use-business-catalyst-web-apps
http://helpx.adobe.com/business-catalyst/partner/web-apps-module-create-custom.html
Thanks,
Sanjit