I compared the Devicemanager of the secure mode with the one of the regular running windows 10 and found out that the problem with the display is caused by the Intel Dual Band Wireless-AC 3165, which is needed for the wifi-connections (It is not loaded in secure mode so there was no problem there).
After deactivating the AC 3165 the display works perfect. For now I use a TP-Link USB-Wifi-stick. Too bad it only works with connected keyboard dock or with the wormlike USB3 adapter.
Maybe I am able to find another driver for the wifi-device.