Emphasis mine.
See that's exactly what the argument has been all along. You are basically going to show us (and believe me when I say I'm interested in your show-and-tell) that we can work really hard to offset the limitations of the Note 3's native camera and camera app. That is like saying "I can show you how to convert a Ford Focus into a Nascar-worthy racer, but you'll have to pretty much abandon the Ford Focus part of the equation."
But I think you've already proven the point of this thread. The native Note 3 camera, using native Note 3 software, is inferior. If we are really willing to pose our subjects, switch software, fiddle with the settings and ask our camera subjects to stop moving, hold their breath and pose nicely....we can improve our results.
Sorry, but that's not even remotely the topic of this thread. I'd still appreciate knowing how to force this inferior camera setup to provide passable shots for the 4 or 5 times I may get a perfect scenario to shoot a vase of flowers by candlelight, but for otherwise its just amusement and amazement....not useful for grabbing quick snapshots. And since grabbing quick snapshots is THE purpose for a smartphone camera.....case closed.
If you think downloading an app from the Play Store, pick a shooting mode that does not force any unwanted processing to your photos, and then simply pick the right ISO right from the shooting screen in order to get better quality photo is too much work, then there isn't much anyone can do to help.
As for shutter speed, pretty much all the smartphones on the market will force the shutter down to about 1/10~1/15 when it deems the scene is too dark, and most do not allow you full manual control (though I will recommend one that comes close). You cannot shoot in low-light with a moving subject with any smartphone or even dedicated compact camera and not get blur--it is a simple photography fact, as all camera products aimed at the average consumer will force the camera to the slowest shutter speed and lowest ISO they can get away with. The manufacturers NEVER program cameras to allow fast shutter speed in the fool-proof automatic mode, unless it specifically has a sports/action mode of some kind that is set for that specific scenario.
Yes, Samsung's app does unwanted processing you cannot turn off, and that is what everyone is complaining about. I'm giving you the solution (and whole ton of information coming in the article, with extensive testing, recommendations, tips, etc), and it's up to you if want to use it. If you just want a fully automatic, fool-proof, point-and-shoot that can take perfect photos even in low-light while the subject is moving around and the shooter isn't even trying to hold the camera perfectly still, then you need to understand that you're asking for something that has never existed in human history, and likely won't for at least another few to several years. Currently, the only way to get close to what you're describing, is the kind of shooting I do with my Canon 5D Mark III, where I use the fastest and most accurate lens I can afford (my fastest lens is f/1.4), set the shutter to manual to match the lens's focal length (so if it's 50mm, I set it to at least 1/60 to counter camera shake, and then even faster depending on how fast my subject is moving), and then either set the ISO to auto or pick one that gets me the cleanest image. That'll get me pretty close to the ideal performance you are describing, but it'll still require post-processing with noise-removal in Lightroom, and we're talking about $5,000 worth of gear.
If you actually have shot a camera that does what you are asking the Note 3 to do, and does not cost a lot of money or require some photography knowledge, then I'd love to see it, because it's probably some incredible alien technology. All the other smartphone cameras on the market have the exact same problem of blurring movements in low-light--it is simple physics. In terms of image quality, some might achieve slightly better results due to a larger sensor or clever processing (or lack thereof), but the improvements aren't exactly mind-blowing, and it still does not address the issue of slow shutter speed forced by the low-light.
Anyway, I'm putting so much time into doing this, and those who choose to make a little effort and try my upcoming tips, will see better results. Nothing I'll be showing you guys will require a lot of work--in fact, I have broken it all down into very simple formula that you can learn in like, 5 minutes, and then apply to all your photography from then on. It'll take you just a couple of minutes to download the recommended app, and then another couple of minutes to set it up, and BAM, you're done.