If you use the logo option on Asteroid Option -> Appearance -> Header Logo then the image should automatically link to the home page. Another alternative is to add a text widget on the header area. You could add an <img> wrapped in <a> tags.

Do you have any idea how I can change the default avatar picture style? It shows as a square picture but I want it to be a circle.

Which avatar? the one on the comments or the one on the author box which is located on the bottom of posts (I see that this option is not active on your site)?

You could add this on Asteroid Options -> Custom CSS

#comments-wrap .avatar {
     -webkit-border-radius: 50em;
     -moz-border-radius: 50em;
     border-radius: 50em;
}