With a slow shutterspeed of 1/10 and an aperture of f/2 at ISO 1600, your exposure is the same as f/5.6 and 1/40 at ISO 25600.
2 stops slower lens + 2 stops faster shutterspeed = 4 stops higher ISO = 4 stops more noise.
Keep in mind none of that is requiring any ultra fancy gear, pretty much all somewhat recent cameras can do ISO 1600 and 1/10 second shutterspeed and f/2 primes aren't exactly expensive lenses either.
More modern or higher end cameras produce some pretty clean images at ISO 1600 (in that example) to begin with.
You can still run a noise reduction algorythm over it to reduce noise at the cost of some sharpness.>>3766000
Depends on the lens and setting.
See my example, a slow shutterspeed and a fast lens make a huge difference.
With a fast prime and slow shutterspeed, modern cameras work pretty well in low light.
Even an EOS 2000D with a YN35 mm f/2 is acceptable in low light if you know how to use it.
A decent setting I'd suggest for handheld night photography is:>fast prime 50 mm equivalent or shorter>manual mode>aperture fully open >shutter speed as slow as you're comfortable with>automatic ISO
And if available, use image stabilisation or weight down your camera.