Would it help the video streaming plan if you were only streaming a part of the computer screen? I'm certain that a lot of people who want to stream video probably want it for playing PC games, so I'd guess that having the option to zoom in on the screen to a specific region, and having the game on windowed mode would help out a bit.
Also, this has probably been asked before, but does the newest CIA version allow the use of the N3DS buttons (C-Stick + ZL/ZR)?
That was always the plan. If an entire desktop eg. 1920x1080 or even a small one like 1366x768 were downscaled to 400x240 (or the appropriate 16:9 resolution, 400x225) it would just be a blurry mess.
If a game is rendered in a window at 400x240 (or 3D at 800x240) it is already pretty small and low quality, but that takes more than 100kbps to stream without losing even more quality.
To demonstrate: I downloaded a Youtube video of Black Ops 3 gameplay at the smallest resolution Youtube serves, 256x144 (64% of the width of the 3ds screen size) and at 15fps. Looking in VLC, I can see the bitrate varies between 200 and 250kbps for the H.264 version - the same codec used for livestreaming. I'm not sure how much of this is audio because VLC won't tell me, but it might be a flat 128kbps. The WebM format of the same video shows them separately as 128kbps audio and ~64kbps video (WebM/VP9 really is a lot more compressed, though the picture quality sliiightly suffers).
To see if it's really feasible to do this through streaming, I decided to try record it myself. I set OBS to record at 100kbps 15fps with the lowest audio possible to choose - 32kbps mono. The output file hovers around 150kbps so apparently this isn't quite doable. At this resolution it seems to not be too blocky though (I've also tested at 400x240, which gave me similar kbps but it looked terrible and blocky). The question is, can OBS be set to leave out the audio completely? Can the stream be optimised down to fit in what's available? Is it only even as good as it is because I set it to save the file, would streaming it be worse? Is there a different livestreaming program we need to do this? The test file is here if you want to take a look, and decide whether that quality is acceptable (remembering the actual result will probably not be quite that good).
https://mega.nz/#!a15GDCwY!N_0LB5QQs7IHoaVCl6vQk4qPwwIGxFnHv1u-vTJbN6w
In short, yes it is doable but the quality will be pretty bad. I am not really sure how to go ahead and implement this (best case, I'm still waiting on the n3ds video api to be added to ctrulib, just skip o3ds support) and I'm not sure if someone experienced enough would bother because it seems like a lot of work for a pretty unimpressive result. I've also looked into coding it in lua which would be better suited for my skill level, but this means the video gets even less compression (basically, each video frame is an individual jpg) so it seems even less worthwhile.
Keep in mind that I'm a beginner programmer who's not very good at C. Perhaps there's a better way to do this, but it's way outside anything I could hope to do soon.
As for your other question: no. I can't compile or test CIA, so it's using the set up CTurt gave it. I've heard it IS possible to let CIAs use n3ds features but this one cannot, so you'd need to ask someone more experienced in this area to take a look at it.