Cat 6 and Romex run perpendicular
Darn near none. Even less if you do it right and run conduit so you can replace it when you can't live without Cat9, or 12 pair fiber, or whatever everyone will have in 5 years.

The whole point of the fancy-pants wire is that it is, in fact, resistant to interference pickup, in places a lot more challenging than your house. Though I hardly see the point of Cat6 - it can barely run 10Gbit, and Cat5e runs gigabit just fine (I have over half a mile of it (in sections less than 100meters, of course) connected to switches that report error rates, which are pretty much 0)