Getting 7 input channels for the thermo-couples is likely because there is one channel used for internal purpose like the cold junction or zero correction.
When testing the conductive ink with sharp probes, there are two contributions: one is the thick film part and the other is the spreading resistance around the small contract. To really check the painted resistance it would likely take a 4 wire measurement.
With the calculator it looks like the one digit that sometimes got to bright probably got a problem (e.g. shorted out common pin). This may also effect the keyboard. There is a visible solder bridge / tin splatter on the board.
I don't think the calculator is genuine Faber Castell, more like an OEM solution. The LEDs look a little like the HP bubble ones. Some 20-40 mA from 4 coin cells in series sounds like a fail, unless rechargeable. The slight rule is a backup when the batteries run out

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