I forget the precise year when the NTE5/A was first released . . . It would definitely be in the 1980s. If I am remembering correctly, it was in 1981 when the plug and socket concept replaced the directly wired telephone installation.
If you can find the location of those two other sockets and then take a look behind them, photographing any wiring that may still be in the backing boxes, it may help us to understand how things have been modified over the years.
IDC3 is just the connection for what was generally called the "bell wire". In a master socket, be it a LJU (line jack unit) or an NTE5, there is a shunt connected across the pair. The shunt consists of a 470 kOhm resistor and a 1.8 microFarad capacitor connected in series. The "bell wire" was connected to the junction of those two components and then extended to every other secondary (extension) socket in a daisy-chain fashion. With modern telephones, it serves no useful purpose and can be the source of poor broadband performance. So the advice is always given to disconnect the "bell wire". (If you critically look at image number 4 you will see that the bell wire is not connected to screw terminal no. 3 -- it has already been disconnected. (Or perhaps it was never connected.))
As for where to connect the modem/router, it is currently in the optimum location, at the end of the "daisy chain", when individual micro-filters are being used (rather than a centralised filter, a.k.a. a SSFP). As for powerline adaptors, please don't consider using them. (I regard those devices as pure evil!)
