Hi Ján,
5.) you change the view to the next week (2015-02-16 - 2015-02-22) => we must show the "floating todos" in the interface somewhere ...
I think this is where the misunderstanding comes from.
If a floating event has a starting date in the future, it should be shown only on the starting date. It behaves as an ordinary, future, all-day event.
If a floating event has a starting date in the past, and is not yet completed, it should only be shown on todays date. It behaves as if it were an ordinary all-day event scheduled today.
If a floating event has been completed, it is no longer shown at all. (Or possibly only on the date it was completed for archival purposes).
So if you change the view to next week, no floating events need to be shifted in confusing ways.
-- Johan