That is helpful. You have a terrible bird's nest of wires to sort out. But sorted they must be.
I suspect that closet was an Ethernet hub, and you likely have Ethernet cables going to different places in the house.
If you are going to use those other cables, which you probably should, then I would install a pro 10"rack in that closet and use a 19" patch bay and 19" Ethernet hub.
The patch bay is on top and the hub below. That room has another hub in the main AV rack. There are smaller hubs in the great room system, family room system and office. That is a construction photograph well before the room and house were finished.
The front speakers look promising. I don't recognize them, or see a manufacturer's name on them. It does not look as if they had grills on them or any facility for placing them.
I think there is every possibility they are home made. If so you have to hope the owner designer was an expert. You will just have to see how they sound and hope for the best. The speakers look to be all the same.
I would check the DC resistance of those speakers, and see what it is. I suspect they are four ohms, which some receivers do not like. The DC resistance should be somewhere between 3.5 and 3.8 ohms. The DC resistance will be a little lower than the actual impedance. If the DC resistance is below 3.5 ohms then don't use them.
It would be ideal if you purchased a
Daytons Tester, and then you could measure the impedance curve to make sure they will not blow up your receiver.
That will tell you for sure if those speakers are lethal or not. We can help you interpret the curves. It will give you the impedance with frequency and the phase angle of the speakers. In this situation I would recommend doing this, as I have no idea of the provenance of those speakers, may be another member will recognize them, but I don't.
Ceiling surrounds is not ideal, and they in the wrong place. I would buy separate surrounds for the sides, placed to Dolby specs. That will give you a 5.1 system with a sub.