Connecting unused cable boxes to existing splitter

Hi everyone,

Just moved into a new house where four rooms have cable boxes installed, however only one of them is connected to the splitter taking in the signal from Comcast. Unfortunately the connected box is installed in the corner in the front of the house and therefore the Wi-Fi signal in the back areas is not great. Before investing into a mesh wifi, wanted to try whether placing my current router in a more central location would provide enough coverage.

Challenge I have is that the box I want to use is not connected to the splitter. I have a few questions:

1. The two unused connections coming from the splitter are blocked with some sort of connector. I tried unscrewing them but they don't seem to come off... Am I missing something obvious or is there a special tool needed? (See picture)
2. Once I have these pre-installed connectors removed, can I simply use a new connector and connect the wire of choice in addition to the currently used port or would it be better to remove the existing working connection? I only need one box to work - only using Internet and no cable TV

This is the first time that I've had a look at "things behind the cable box" - apologies if I'm unclear or asking obvious questions. Please let me know if I can help with any more details.