What I don't see is any documentation on what we call a "wiring plant." Without documentation you have to be well seasoned to know what is likely what.
But the biggest mistake is to take what works (I take it this works now) and make it neat. If you have networking background you know that being shown a cable plant is not enough detail. Where's the design, the notes, the sketches? Usually none so you redesign as new.
As to WiFi, why not fix what you have with a second WAP or move to a Google Mesh system?
Recently I moved into a new home and since then I have been using wireless which has proved unreliable. I now realize that the home has cat 5e cabling already run throughout the house, but upon inspection in the basement I realized that the home has some sort of a structured wiring panel already set up. I have no idea if it supports internet or just phone, but all I would like to do is set up a few of the ports in the home to connect to the internet. Can I use the setup, or if I will have to take out what has been put in and re-terminate the wires and connect them to a switch? If I can use the setup, any suggestions as to how to go about it, what type of switch to use, and how to make it as neat as possible would be appreciated. I would like to get decent equipment as long as it is not too expensive. I will respond to any questions and thank you for your help in advance.