Most of the replies were written before the 2nd and 3rd images where there. They provide some very interesting comparisons. Number 2 is the original full size, number 3 is cropped from 2.
So the real comparison is 1 and 3.
Shutter Aperture ISO Focal Length
------- -------- ---- ------------
Image 1: 1/160 f/22 1600 65mm
Image 3: 1/30 f/4 100 28mm
Difference: +2 +4 -4
The exposure is increased by 6 fstops, and the ISO sensitivity reduced by 4. Hence there is a 2 fstop increase in brightness. That is probably just a little too much! But the difference between over exposing slightly at ISO 100 and under exposing significantly at ISO 1600 is very obvious in the amount of noise. While the first image did not take well to being cropped, with the second image cropping is not so much of a problem.
But the real trick to all of this is not to memorize this as a set of facts that one tries to repeat, and instead it is an example to help learn why each component worked towards the end result. Being able to look at a scene, measure the light, and decide what mix of the various parameters will produce whatever result is desired.
For example, the first image had the advantage of requiring less cropping, and thus getting more pixels on the subject, due to the longer focal length used. Given the lens available, perhaps instead of a 65mm focal length it would have been better to use 130mm or even 200mm. That would provide much higher resolution and lower noise.
Another difference that might be useful would be more Depth of Field in the third image (purely a matter of taste). To do that stopping down to at least f/11 would be better. Along the same lines, the shutter speed of 1/30 of a second works fine for, ahem, elderly gentlemen but if this were the grandkids it might not be fast enough. So the 1/160 of image 1 might not even be fast enough. What it comes down to is realizing that ISO 1600 is in fact usable, but only if the image is not under exposed!
The extra 2 fstops of exposure provided for image 2 is not critical at ISO 100 where the dynamic range of the camera is greater than that of a print by 2 or even 3 fstops. At ISO 1600 the D7100 has a useful dynamic range of about 6.85 fstops, which is probably just about exactly the same as print, and that makes precise exposure very critical.
Using ISO 100 is fine for this particular shot, and the 2 fstops of slop for for expose makes it easy. For other cases with the same light but needing different results... using ISO 1600 may be necessary!