@Praxie
Is it possible to connect to the projector in some other way? (USB-mouse, bluetooth etc.)
Yes, both USB-cable-mouse, USB- bluetooth-mouse
Is it possible to switch to the HDMI1 mode as soon as HDMI cable is detected?
Yes, when you enter the HDMI page, please press the menu button on remote to switch the HDMI version. and please check the HDMI version-menu bar at the top of home page.
You can contact service@xgimi.com to purchase a new remote