Idea 1 COULD be possible, but way to much work for a simple homebrew and patching things stored in NAND (stock apps) can end up in bricks, so not worth it. To download stuff, you can go with MultiDownload++ though if you know the link to the file. For idea 2, I think there already is one for .zip and same for .garc and .narc (both of which have absolutely no reason to be opened on the 3DS btw).
You CAN download select files (eg: certain pictures), so it IS possible, just would take reprogramming a large chunk of code.
That would be a nice idea and since it's a homebrew (meaning it runs as a game instead of along with a game), it can even be extended-memory and end up really strong. But again, not worth the sheer amount of work it will take. Also, why use the 3DS for browsing? Even a terrible phone can do more