Thanks for your detailed explanation.
ad) manual refresh of every cageory and page without a) figuring out first which need to be updated
Yes. You can use "orange" button "Refresh All Pages" on tab "Action" in the M-Turbo administration.
I dont have a button "Refresh all Pages" on the Actions Tab. I have 5 buttons, see attachment, do you mean "Cache all Pages"
ad) manual refresh of every cageory and page without updating everything in the entire url list.
I'm sorry. But I don't understand what do you mean. You can use the download script for daily refreshing all pages. One of its arguments is the file with the list of ulr which have to refresh. You will find it in directory "app/code/local/Artio/MTurbo/Model/scripts/".
When I click "Cache all pages" it recaches every page regardless of whether it needs to or not. This takes hours in my case. I was looking for a button to press which would only cache "changed" pages.