Are 3DS games and progress backed up to your Nintendo Network ID?

So, the other day I was playing on my 3DS and I set it down to grab some food from the fridge. In the not even three minutes I was in the fridge, my sister knocks the 3DS off the counter into the wall with such force it snaps the top half off the bottom (she was running really fast), and my SD slot isn't the best at holding the card in (I have to hold it manually when I play) so the card shoots out and then she unknowingly steps on and snaps it.

I normally am a very cautious person when it comes to saving and backing up but with my Fantasy Life game, it had no back up (I checked). I was like level 140 and had creator ranked all but three classes, and I would rather not lose all of that progress, or even the purchases I made for and in the game. So is it possible I could buy another 3DS and link it to my NNID and reclaim my progress or even just my purchases?

Save games are not saved to your NNID. The only things stored there are which games (and DLC) you have purchased. You can redownload purchased games, for example.

Saved games are stored on the SD card (for digital games) and on the cartridge itself (for physical games).

I'm not sure exactly how you'd connect your NNID to a new 3DS, but I know it's possible as I've seen other people on this site do it. Try contacting Nintendo customer support, they're very helpful about this sort of thing. They could also tell you how to get your ingame purchases back if that isn't redownloaded.

The only way I know of to backup your save games is by either manually copying the contents of your SD card to your computer (for digital games) or using a third-party device such as Powersaves (for physical games). But if you haven't done either, I'm afraid you're out of luck.