Yes, you can -- I usually say either "pretty well" or "pretty good." (Technically, "pretty well" is more correct, but "pretty good" is more common and sounds more casual, at least in the US.)

You can say that but "pretty" introduces an element of doubt, making it sound like maybe you aren't so well. In the U.S. we tend to exaggerate how well we feel. In response to "how's it going?" people are likely to say something like "Great!". If you are only "pretty well", I might think things are only so-so.

Yes, you can !!

Yes, it's a good answer to this question!

Yes, it sounds very natural.