Replacing the flat cable from the splitter to the Cat5 with Cat3 with RJ11 on one end and bare wire into screw post terminal on the other made no difference according to the line stats. I don't know what I was expecting to see, but I suppose increased resistance to noise is a good thing since I cannot predict it. All my findings are on quiet Saturday evening and Sunday afternoon when the nearby laundry machines and fluorescent lights were not operating.
As for the round phone cord, the only thing I can make out is "TIA568B2" and "Cat.5 28AWG". I put this between the wall jack and the modem and compared to flat cable, I did not notice any difference.
Here is Cat3 from the splitter to the Cat5e
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i.imgur.com/0SdsZ.pngFlat cable at the same location.
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i.imgur.com/XTY8L.png