How to install my Ubiquiti gateway into my Telus fiber home network?

Hey guys, I want to move away from Telus' equipment and install my Ubiquiti UCG-Fiber and U7 Lite access points.

I currently have fiber internet, Optik TV with legacy equipment, and a home phone.

In the network panel, I have a Telus-supplied NAH, WiFi booster 6E, and some splitters. 

What is the purpose of the MoCA port on the NAH?

I have no idea why there are multiple splitters installed and with RG-6 cables on them. I want to clean and tidy up the network panel as it's a total mess.

Is it possible to remove the NAH and plug the ONT, legacy TV equipment, and home phone to my UCG-Fiber? I know the internet works if I connect the ONT directly to the UCG-Fiber's WAN port.

If not, is the best case scenario to leave the home phone and legacy Optik equipment with the NAH, and then bridge one of the LAN ports and connect that to the UCG-Fiber?

Not sure what a NAT and double NAT are, but will this problem occur with this setup?

I have no interest or desire to install Rogers' Internet service. For my security, is there a way to unplug Rogers' equipment from my house, or if it's a condo? I'm contemplating installing MoCA adapters.

Looking for advice on how to best optimize my new home network/topology.

Thank you!