What lighting you use is not as important as how you use it.
However, strobed lighting has a technical advantage over continuous lighting. That advantage is the ability to control the ambient light exposure separatrely from the strobed light exposure with a single shutter release.
I would recommend you start by leaning the basics of photographic lighting. A very good book for that is in effect an introduction to photographic lighting;
Light Science and Magic, Fourth Edition
All of the images appear under exposed. For a portrait, skin highlights should be between 235 and 240 in the red channel.
In the top photo you used the following camera settings:
f/5.6
1/2500
ISO 3200
Because of the high ISO and under exposure there is a lot of image noise.
You didn''t need a shutter speed of 1/2500. By using a slower shutter speed (4 stops worth to 1/150) you could have also lowered the ISO 4 stops from 3200 to 200 and gotten the same under exposure. To get 240 on the red channel on her left cheek highlight I had to add 2.75 stops. So for a correct exposure you would have needed your ISO at about 1200.
Using a tripod though, you could have reduced the shutter speed even more to 1/75 and also lowered the ISO to 600.