Hi Paul,
As Eric says that is most certainly non-standard wiring. The grey cable with writing is not a normal BT supply which indicates that a non-BT person has done this wiring in any case.
It's difficult to say exactly what the official position is re the wiring in this configuration.
Assuming that the orange wires are not connected to pins 2 and 5, and that you are allowed to adjust those wires on the front plate, there's a good case for removing them IF they are only the ring wires.
The correct configuration is as you describe with the incoming pair only connected to the two screw terminals at the back and any extensions should be connected to the front plate.
As you say there are three extensions it probably means that some are "daisy-chained" in series, unless you have more than one phone line ? You can determine whether this is so on BT wholesale supplied lines by dialling 17070 and listening for the lady to tell you "This circuits is defined as 01 xx xxx xxx".
You might also find, as it is a block of flates, that BT's cables are terminated elsewhere. If this were a standard BT house installation you would expect to see single colour wires in a drop wire cable, only connected to the back. The fact you have blue / white striped wires might suggest there is another BT Distribution Point which could be a 10, 20 or possibly even a 50 pair cable.
Kind regards,
Walter