Hey Martin,
No, the interface will show the state of the CNC controller program. You may start a g-code program on one instance and stop it on another.
Yes. I don’t have a monitor on the controller, only remote access through ethernet, but with two remote instances, they show the same states. In doubt, you can press “refresh” as the interface is a web page in a browser.
What you cannot see in another instance is the MDI command history of a specific instance.
I think it is an advantage to connect via Ethernet, even if the laptop/computer is directly beside the Onefinity CNC machine, because you see the 3D toolpath simulation and you never have to deal with USB media. If you have a smb share somewhere in your network, you can drop your g-code files there and upload them to the Onefinity CNC controller with the “Upload new g-code” button on the user interface in the web browser on any remote computer.
What you need to install an Ethernet local network in your home 
- CAT-5 SF/UTP Ethernet installation cable with TIA-568 pair coloring
- 8P8C wall socket with both T568A and T568B color indication, for LSA-PLUS quick connection
- LSA-PLUS Tool with belt holster
- Knipex Ergostrip Universal Stripping Tool
- Pozidriv Screwdriver
Phillips Screwdriver - Heller Masonry / Concrete Hammer Drill bit
- ISO cable clamps with 20 mm steel pins for 5-7 mm cable diameter
- Three-and-a-half ounce (100 g) Warrington hammer (also called “telephonist’s hammer”) (Footprint, Sheffield)
Who needs WiFi if you own a hammer drill? 
If you connect the Onefinity CNC controller to your local network, you can access it from the other computers of your network, and g-code files can be uploaded via the computer you are on. If the latter has access to a smb share on any other computer, you can also upload files that are on other computers. Of course you can open the Onefinity Controller in one web browser tab and surf in the internet in another tab.
If you have a router and public internet access via ISP, you may or may not allow the Onefinity Controller to access the internet. If you do this allows the Onefinity Controller to check for new firmware. In the other direction, if you want to access the Onefinity controller from the public internet, you need a port in your internet router that is open to the world. Usually internet routers are configured to be “invisible” to the public internet and not to have open ports, because that is a potential security risk but you could set up a VPN like people do that need access to their computer from outside over the public internet.