Next question is, how long does the cable need to be to store the content of the entire internet and get rid of any other storage?

The entire internet as a circular buffer in a very long fiber cable. Just wait for your content to appear. :)

https://live-counter.com/how-big-is-the-internet/ puts the size about it at 23 million PBytes. 1000PB = 1EB, so 23,000 Exabytes

At 200 exabits per second, or 25 Exabytes per second, it would take you a thousand light seconds to send the entire contents of the internet. With the speed of light in the cable about 2/3rds of C, that would require about 600 light seconds of cable, which is about the distance from the sun to the earth.

Quick googling tells me the typical diameter of an undersea cable is 25 mm. If we assume let's say 15 mm of that is actual fiber (wild guess) and approximate them as a single cylinder that works out to only about 0.03 km^3 of glass... that's a lot more feasible than I was expecting. Comparable to the volume of concrete used to build the Three Gorges Dam. I suppose it's only that "reasonable" because we're talking about a hypothetical 200 exabits/s, puts into perspective just how fast that is.

https://www.wolframalpha.com/input?i=pi+*+%28%2815%2F2%29+mi...

Related video, using pings to store data: https://www.youtube.com/watch?v=JcJSW7Rprio