Ow. I would assume that this is a symptom of poor ground-bonding. Somewhere near where the cable enters your home, there should be a connector that bonds the cable’s shield to ground. It may simply be a fancy barrel-connector with a screw terminal on it. There should be a wire running from that terminal to a spike in the ground nearby.
But I’d hope that your service tech would have checked for this.
Yes. Data services require “bidirectional” splitters, capable of passing signals in both directions.