This is neither.
Lots of 3D (fast) Fourier transforms
Again, interesting, we do a lot of this at work. Complex 3D FFT transforms. I write my plan and processing code using CUFFT. I'm curious as to whether they'd be using fully custom code for such a large computer. We're only using 8x Tesla cards at work.
They can tap it. They do tap it. They're building a nationwide infrastructure to capture all the IP header data at each point where it enters a telecommunications network. YES, THEY CAN DO THIS. THEY ALREADY HAVE DONE THIS. THEY DO THIS ALL THE TIME.
The C64's operating system is stored on ROM chips (which by definition can not be written to.)
How do you explain EEPROM or flash ROM? ROM is a narrow context.
If mathematically you end up with the wrong answer, try multiplying by the page number.