data-wiringethernetinternet
My apartment is currently wired with five Cat5e cables that all meet in a closet, where there is also an outlet and the cable entry. The ethernet is currently wired into the board in the picture below.
I want to move the modem and router from my living room into this closet and distribute the internet from there to other rooms using the Cat5e cabling. Can I use this existing wiring setup or is it best to remove the board, manually add jacks to each cable, and connect those to my router?
From this photo:
Cable modem is likely attached to the cable at the lower right corner.
Cable modem network jack goes to the internet port on your router.
Lan ports on the router are connected to the patch panel in the center. The yellow cat5/6 wires are networking to the rooms.
If you want TV's in different rooms, you can swap out which white cables are plugged into the top splitter (or get a different splitter with more ports, but the fewer times you split the signal, the better the signal is). The bottom splitter is the first split to the cable modem to give it the best signal. Yellow cable line is most likely the source, and white cable lines go to the various rooms.
Blue wires should be for telephone. I don't see where the external connection is, so if you don't have a dial tone, it may not be connected to the demarcation outside. If that's the case, either the last owner never used it, or they plugged in a voip box into a network and phone jack elsewhere in the house.
Without knowing more details, your plan is reasonable. Network equipment in the garage is not ideal, but not terrible, especially if insulated. On the other hand, if you live in a hot climate, the heat in the summer will be terrible for the gear. Cold is much less of a problem, though extreme cold would be.
One minor change is to add a patch panel between the switch and the drops to the rooms. This allows you to punch down all of your cables, rather than terminate them with jacks by hand; punching down is much easier for the novice (and the extra cost is minimal). You then run short cables (you purchase, not make) between the patch panel and switch. See my answer to a similar question for more details about using a patch panel.
Depending on how the house is laid out, and how much slack there is in the unterminated cables, you could take the whole bundle and move it somewhere inside the house. If there's little slack, you may just move them to the other side of the wall they're currently on. All my network and CATV stuff is in the master closet for this reason.
Brand recommendations are off-topic here, so I won't comment about specific routers or equipment. As far as testing the network, you should just need the gateway connected to test the fiber install. The rest is on you and can be done later. A simple network tester (example only, not a recommendation) will verify all your punchdowns are made securely, though that won't verify gigabit speeds.
As for multiple wired devices in one room, yes, a small 4-8 port unmanaged switch will work just fine.
Best Answer
It looks like this was originally intended for telephone service distribution.
There's a few ways to go about it depending on how neat and tidy you want the job to look.
You should trace and label those cables as well so you know where they go.
It's likely that one does not end in your apartment, but is going to the street or a patch panel elsewhere intended to provide phone service. To prevent damage, do not connect this one to your network equipment.