The faceplate with a square hole could be used for just about anything, so that doesn't help.
Let me just say that pre-wire in homes generally consists of a few types of wire:
1. 16/4 wire which is just a sheath with 4 individual conductors (red, green, black, white). It's just wire. It can be used for anything. One sheath can be used for 2 pair of speakers because there are 4 wires. By convention red/black for one and green/white for the other. It is also used for security systems, remote controls, tying smoke detectors to your security system, etc. Again it's just wire. It was probably
intended for speakers but that doesn't mean it must be used for speakers.
2. Coax cable - RG59 or if the place is newer, RG6. This is your standard cable used for the cable tv system. It is also just wire and can be used for other purposes. Usually they terminate it with the standard 'F' connector (the type with the little pin in the center that you use for your cable tv hookup), but often they just leave the bare wire in the wall. You can terminate it with RCA connectors and use it as a subwoofer cable or even as the cable to connect the pre-outs of a receiver to an amp located in a different room where the wire goes.
3. CAT5 - this is wire that has 8 conductors and is used for phone and/or network connections. If any of that wire exists, you will almost certainly have a network connection center somewhere in the house where all of the wire terminates (mine is in the master bathroom closet). They are supposed to follow conventions like blue wire for data and green wire for voice, but of course they never do.
There is virtually no chance that any of those wires you see that are not terminated have to be connected together to tie the first floor to the second floor or anywhere else. The speaker wires simply start somewhere in the living room where they assume you will place your equipment and go to the other floors where there are speakers. The coax cables are probably in every room where you might want a tv and either go to the central wiring closet or are installed in series as one giant wire where you just tap at each room.
The only way to be sure what is what is to trace the wires. You can do it the hard way by carrying a tv around to test the coax or hooking up speakers to the speaker wire. Another way is a tone and probe generator kit which can be found at most electronics stores and places like Home Depot and Lowes. I bought a cheap one called the Lan Tracker at Home Depot and it worked well enough for me to sort out the mess of my install because of course there is no documentation whatsoever about which wire is which.