* Is it possible to create sub-categories and how?
Yes; it's described best at Meta:
http://meta.wikimedia.org/wiki/Categories#Subcategories
* If I look at a page with the Category footer, and I
click on the Category
it links to edit the page. And not just to a category overview. But it has
members.
A category page is basically just like every other wiki page. The only
difference is that category pages also list all pages belonging to the
respective category.
Since no content (other than that automatic listing) exists for the
category page by default, MW will take you to the edit mode to create
this page.
FWIW, this issue has been discussed in the "Red category link is
unhelpful" thread.
HTH.
-- F.