Lots of questions! First make sure windows can see and use your screen. Then configure in Resolume. Why did you buy a USB c to HDMI? I’m not familiar with your laptop, but ideally you want your main graphic card to run all three screens (laptop, LED screen and new screen). This will probably mean us...
I’d be more tempted with an Aja HA5-4K hooked up to your main GPU with a decent HDMI cable. You can then use eithe of the options you outline above. For option two you would simply duplicate your output slices and move them to the “spare” part of the 4K output.
Haven’t tried one of the newer usb c/tb3 MacBook Pro’s yet, but my gut feeling is that a Datapath FX4 will give you the smoothest output. Just use one good quality tb3 to DisplayPort cable and then set the FX4 input edid to 3840x1080
I think Arvol meant “how much more expensive is the 1060 compared to the 1050”. Worth spending as much as you can once, rather than regretting it later on.