Created a user role for only contact management, stuck with 4 menu items having only the same contacts,accounts

I wanted to disable/hide all unnecessary functionality from someone that is only adding/modifying some contacts. So I created a role and disabled most entries there and assigned it to this user.

Annoying is that the sales, marketing, support all show the same, and activities shows a bit more. How can I hide sales, marketing, support from this user?

The sales, marketing and support menus/submenus are not really useful in that case.
You should edit the profile of that user and uncheck Module Menu Filters in the Layout options tab.

Here are some post that might help you to solve your issue: