I have got two new problems to solve.
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Problem #1
First scenario (only one menu item):
Menu Item
Title: Category List
Type: List Of Categories (Categories View)
Tab: Page Display: Show Page Heading = Yes, Page Heading = "Category List"
Page heading shows the correct title "Category List" while in categories list.
After selecting one of the categories from the list,
the page title should be e.g. "Category Details" but it still remains "Category List".

However, In some cases it's necessary to access a particular category via a direct link.
Problem #2
Second scenario (additional menu item):
Menu Item
Title: Category 1
Type: List of Files (Category View)
Tab: Page Display: Show Page Heading = Yes, Page Heading = "Files in Category 1"
Funny: In this scenario page heading is correct in categories view AND category view,
BUT - You cannot return from category view to categories view (up button points to current view).
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Regards Mike