This widget displays the recent posts on a category page for that category
The widget will be displayed only on the 'Category Archive Page'
Yes. You can style it as required. The recent posts list are wrapped in an unordered HTML list having CSS class ".tm-recent". The excerpt is wrapped in a div tag with the CSS class ".tm-excerpt". The complete widget itself is wrapped in the CSS class ".tm-cat-recent-post"
The Read More link is wrapped in the CSS class ".tm-read-more-text". You can style this class n your stylesheet.