Is there a component or a module or a plug-in that could allow users to register setting also an e-mail address@mydomain.* and an e-mail account password? It could be cool if the e-mail account is created automatically (nickname@mydomain.org) and the passeord is the same inserted in the registration form.
Let me know!

PS. Sorry for my bad english.

The short answer is yes.
I have this employed on my site with a combination of using mambomailpro and some hacks to joomla itself to enable dual email accounts. The end result is that a user has a primary email account (The one for initial registration and the main contact account) and is also assigned a secondary email address (userid@mydomain.com) that is automatically created for each user upon successful registration. Once registered, all email addresses that are displayed and used in communications with other site users revert to the secondary email address thus cloaking the members primary email address and reserving that for internal administrative purposes.

THis is a custom hack and not a plugin or component as it requires a direct hack to the joomla core files. But it works effectivly.

Like all things when constructing a custom website, some learning by the owner is necessary.. We all did it in the days before CMS systems, and we must continue it today to achieve some of the results we're looking for. SO, dig in, get dirty, hack some code and see where it takes you.

But it can be done