user data that is stored as user properties in an item is stored IN this
item independ if the same user property is defined in the folder.
I need the additional definition of properties in the folder with the same
names if I want to use filters and to display these data in a view?
Correct??

Not quite. You need the same properties, not additional properties -- same
name, same data type. They just need to be defined in the folder, as well as
in the item.

The user properties stay with the item even when I move it to a different
folder. Correct?

Yes, that's correct.

If I send an item with user properties to someone who has not the same
form installed he will not see the user defined field, but the data is
still in the item? Correct?

In many cases, not correct. See http://support.microsoft.com/?kbid=907985,
the section on "Behavior changes in Outlook."

Is it enough to install and register the form region on an other computer
to access this user data?

No, registering a form region or publishing a custom form does not create
any folder-level property definitions.
--
Sue Mosher, Outlook MVP
Author of Microsoft Outlook 2007 Programming:
Jumpstart for Power Users and Administrators
http://www.outlookcode.com/article.aspx?id=54