As you probably know, all wiring past the NTE5A belongs to the end user and not OpenReach. So why don't we try to resolve the problem of your non-working telephone extension sockets?
I, and I'm sure others, would be far happier trying to assist you in getting your modem/router operating correctly by using an Ethernet connection to it. And to do that you will need to use the tower system, upstairs.
Would you be able to take some pictures of the telephone sockets and the wiring? Start with a general view of the NTE5A. Remove the two screws that secure the end user, lower-half, faceplate. Take a clear picture of the wiring attached to the back of that face plate. With the face plate still disconnected, follow the wiring (if visible) to the first extension socket. Undo its screws and take a picture of the wiring. Continue doing so for all the other extension sockets. Once done, post the pictures in a publicly accessible place and tell us its location.
For the time being, do not bother to refit the lower-half faceplate to the NTE5A. Just plug your microfilter directly into the test socket . . .
Once we've all had a chance to look at the pictures, the next steps could be quite straightforward.
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100% Linux and, previously, Unix.