Date is considered after noon (12:00), but it should be after midnight (after 00:00)

Bad solution: use for date pager the Date field with Date type: Date only not Date and time.

I'm not 100% sure, but I think that the reason for this is that all dates are handled as UTC in date_pager . German summer time is +2

You right!
But how to setup module withe date and time field?

Please review the related issue