I can only tell you from my own experience...the quest for good quality, low light photography without using a flash gets very expensive.
Starting with the exposure triangle: aperture size, shutter speed, and ISO, each has to be increased towards the maximum 'limits' of what you have.
Maximum aperture (lowest f-number) in the f2.8 area or lower. This will allow the maximum amount of light through the lens. Having the lens wide open, however, has other issues, such as narrow depth of field, or, as I think of it: plane of focus. Also, most lenses aren't their sharpest when wide open. Note, too, that f2.8 lenses and those down to the f1.2 range quickly become rather expensive. Name brand, fixed focal length (aka 'prime') lenses that are f2.8 and 'faster' (lower f stop number) start in the $400-ish range and go up from there. Zoom lenses that are f2.8 are correspondingly more expensive than primes.
Maximum shutter time, eg, slow shutter speeds. Dealing with living creatures, shutter speeds longer than about 1/125th of a second may cause a blur due to subject movement, even very minor movement. Even people 'standing still' may sometimes move just enough in that 1/125th of a second to cause a blur. Photographer hand movement is also an issue, so many lenses now have stabilizers to somewhat neutralize the effect of hand/camera movement. A tripod is best to prevent camera movement during longer exposures. As a tripod is frequently too inconvenient under some circumstances, I've managed to 'get away with' using a monopod while leaning against a wall or seated. Although I've done a fair amount of people pictures at 1/40th, 1/30th and even 1/20th of a second, the keeper rate is in the 'dismal' range with subjects due to movement. Think 1 in 20 or thereabouts.
Lastly is ISO, the 'speed' at which the camera records the image. As you have noted in your own pictures, the faster the ISO, the more multi-color 'speckling' occurs. This is referred to as 'noise'. Depending on what camera you are using, ISO 800 may be the practical limit before noise becomes too noticable. Other cameras, ISO 1600 or even 3200 produces relatively little noise. Most recently, cameras can shoot at ISO 5000 or 6000 with little noticable noise. As can be expected, the better-performing cameras don't come cheaply. However...most post processing programs available have some 'noise reducing' capability in them. They can correct some level of noise without causing additional problems of their own. So it isn't always necessary to buy a $3500 camera to get the top ISO speeds when a $1000 camera will suffice when noise correcting software can sufficiently clean up the image.
The obvious and probably the least expensive solution is to get an external flash and learn to bounce and diffuse the light produced effectively. Photography is all about light, regardless of what 'kind' of light it is. Learning to use that light effectively is what photography is all about.