The existing cable being 'colour' and 'white and colour' pairs indicates it's some sort of twisted pair cable, which is what you want. It doesn't matter whether it's CW1308 (telephone cable) or Category 5/5e - it will do the same job.
Of the six wires, only three do anything - 2 and 5 are the line itself and 3 is the ring wire. Almost every phone you encounter today doesn't need the ring wire connected - but let's not get into the technicalities of the ring wire as yet.
From what you describe, the extension to the Sky box is unfiltered, which is not helping, not least because the sort of plug-in extension you describe often does not use twisted pair cable. Before doing anything else, change the order around: plug the filter into the master socket, the Sky extension into the filter, and the phone into the socket on the Sky extension. Has that helped with the disconnections when the phone is in use?
Rather than the filter you suggested, I'd use this one
- it's a later redesign of the one you mentioned, and is the filter supplied by BT Openreach when installing FTTC. It goes in between the existing front and back parts of the NTE5 master. Before placing your order, check the existing screws holding on the front plate of the NTE5 - if they are fine thread pitch, you'll need longer machine screws
(if you're not sure, order them anyway for the 20p they cost).
The existing three pair extension cable to upstairs has enough pairs to use a faceplate filter. All you'd need to do is pull 1 and 6 out of the existing faceplate, and move them to the 2 way IDC block on the filter I suggested - see the yellow arrow in the bottom right picture on this page
for the location. You don't need to disconnect the other four wires - use the slot in the bottom of the filter to fit the new filter without disconnecting them.
At the bedroom end, replace the existing faceplate with an RJ11 and secondary phone faceplate
. Connect the orange and blue pairs of wires to 2 to 5 on the phone module, using the colour code you posted. The green pair of wires go to the middle two positions (3 and 4) on the RJ11 module - it shouldn't matter which way round. You now have an RJ11 socket to connect your DSL equipment to and a phone socket, with no need to use any plug-in filters anywhere.
You will need an IDC tool to make the connections. The plastic ones are awful - it's well worth the money for the knock-off of the official Krone tool
. On the proper or knock-off tools, there's a hook that swings out from the handle - use this to pull the 1 and 6 wires out of the existing faceplate and the wires out of the existing bedroom extension to prevent damaging the connection blocks.
A later enhancement is to replace the plug-in extension to the Sky box (which you can plug in to the faceplate to start with) with a hard-wired one. The cable in these plug-in extension kits tends to be of poor quality - I'd run new twisted pair cable (CW1308 phone cable or Category 5e - it doesn't matter which) to an IDC secondary phone faceplate (many options exist - this
will do fine).