Like the other posters said there are many different types of setups and it sound like you have a double NAT which is why it's not working.
The first thing I'd do is hard reset your Verizon router and connect that to the ONT first. Once it is up and working, reboot all your set-top boxes then they will be back online. Log in to the FiOS router and turn off the wifi.
Next Google setting up your TP Link in Access point mode. By doing this you will only have one DHCP Server which will be your Verizon router. The TP Link will only serve as a wireless AP.
That will fix all your double NAT issue and everything will be on the same subnet. Also if you decide to get FiOS TV One you need the FiOS router first in line anyway.
The red Video light on your ONT means the video light levels coming into the ONT are lower than they should. That won't have no impact on the FiOS app but it could translate to bad RF readings on your home coax cables. I would schedule a tech visit to fix you fiber issue and clear that red light.