Can someone tell me what exactly "using CDN" means?
CDN = content distribution network.
A few years back large data using sites noted their web services were slowing so they booted all the big images, videos, audio and such to other servers geared for straight downloads rather than paying for the fatter pipes and storage and what have you. Games being bulk data are also suited to this.
In this case it was noted that the 3ds could still download content from said CDN and then activate it/run it afterwards with a hacked 3ds. It gets a tiny bit more complicated but in essence it means Nintendo basically ran their own ROM site, one of the best in the world (complete, fast updates, fast downloads, great uptime, no ads, no nonsense) that responded to/ran from their own devices.
They were not the first -- the xbox 360 xbox live arcade (XBLA) would download demos that were actually the full game and could be converted by homebrew boxes by changing a couple of bytes, though in the case of the 360 you would need a legit one to first download the thing (and then transfer it to USB or something). There were also types of DLC that was made into PIRS DLC for some game of the year discs and things like that which could be installed by anybody, even on a stock system. The PC had seen things like it for years as well, at one point in time the demo exe file would often be less protected than the final release so install game, swap exe, then essentially have nocd crack from the devs themselves.
Apparently they upped their game a bit for the switch and some of the things that worked on the 3ds will not apply here that is a different discussion. A slightly older but still accurate enough analysis can be found
https://www.reddit.com/r/SwitchHacks/comments/759myu/the_eshop_and_cdn_explained_switch_edition/
The ToS is a silly paper. It got no weight in the EU.
TOS presented after the point of sale have no weight in the EU according to various court rulings, and there was another quirk where no returns being given effectively forced the same result. Terms presented at point of download/at point of sale/sign in/sign up is a different matter entirely. There may still be terms that run counter to various rights that a court would shoot down but that is a different matter again, and I am not sure of anything that would say they have to allow modded devices on that.
Not your quote but saw it before. The 2 years or whatever thing refers more to online services being shuttered for avoidable reasons during that period. Nobody is obliged to allow you access to a private luxury service regardless of actions taken on the part of the user.