Is Voyager I’s reduced data transmission rate as described in this article because of the distance or because its transmitter getting older & slower?
Transmitters don't slow down as they age. Red shift isn't involved, at all. As a transmitter gets further away the signal at the receiver gets weaker, so it's deliberately slowed down. Data channel capacity depends on signal to noise ratio and bandwidth. As the signal gets weaker the data rate can be slowed to reduce the necessary bandwidth. Noise doesn't increase: it's just a loss of signal strength at the receiver. Narrowing the receiver bandwidth reduces the noise received, but also limits the information bandwidth.