Yes, it features a hardware streaming engine for live broadcasts via Ethernet while simultaneously recording H.264 files to USB-C flash disks.
No, it supports a maximum resolution of 1080p at 60fps. It will automatically down-convert 4K HDMI input signals to 1080p for the broadcast.
You can connect up to 4 HDMI cameras or computers. All inputs feature internal frame resynchronizers, so you can mix and match different video standards.