It is or was pretty common to pull 2-3 cables on every run; cost little and provided for all kinds of upgrades. It wasn’t that long ago that every “computer” item in an office would have its own jack and run back to the hub, rather than using a switch or hub in the office for distribution. Many older buildings have 3-4-6 parallel network runs to every office.
Your next best friend is that sniffer. Go around and pull apart all the phone and cable plates in the house and figure out which ones connect to which. You might also find coils of unused lines behind the wall where the master panel is.
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This. You basically can’t send video over unshielded wire. The whole thing looks like standard connectors used in non standard ways… which is common in niche applications like home automation and networking.
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It’s a balun, designed specifically for putting composite video on unshielded twisted pair. Standard, but uncommon. There needs to be a mate to this at the other end of the cable.
A balun is designed to couple a balanced circuit to an** un**balanced one - most typically coaxial antenna feeds to the flat-wire ones used in days of yore. It doesn’t do anything particularly magical about keeping signals clean or level.
I’ve never seen a balun used for anything but UHF/VHF broadcast and distribution signals. The processing that’s applied to those signals to extract the baseband video and audio will tolerate a degree of noise and interference. Sending video over unbalanced, unshielded wire will transmit every bit of noise, interference and signal variance to the displaying device. Beginning, in most cases, with strong 60 Hz powerline hum and video bars.
Here is an example of baluns used for HDTV over CAT5.
Years ago, I made my own VGA over CAT5 (no baluns) cable and it worked fine for a 30 foot PC XGA signal to my XGA DLP projector. The wiring shown in the OP would have worked fine for 480P - perhaps even 720P.