Author Avatar - This isn't one of the basic options in your layout editor, but there are workarounds you can use to accomplish this. For instance, if you set the author avatar as the featured image, you can then use that in your layout. There are other ways to accomplish that, but that is probably the simplest way to do so.
Show Number of Posts - This you can definitely do. You can just add this option to your layout (Author Info > Number of Posts Authored).
Post Order - You can select the order in which the posts display. Most recent comment isn't one of the options, but you can order by the number of comments a post has.
Hope this answers your questions. Please let us know if you have any more!