1- Edit Article list in User Profile. I would like to get rid of the Category column and add at least one: rating (rating is available for my web's articles).
It's template driven display now. You can find the CB Articles template files below.
components/com_comprofiler/plugin/user/plug_cbarticles/templates
2- Include the number of articles from each user and include it in the User list. I know this number is accessed by CB, since it appears in the User profile. I would like it to be a counter, just like the "hit" field, for example.
CB Query Field would be the ideal way to do this as you'd just query for that count and can then display it on a userlist as a regular field. Aside from that there's no other way to obtain that information beyond querying for it.