Background Color of Excerpt

Go to Asteroid Options -> Custom CSS and add this code

.blog-view {
    background: #8FB7FF;
}

Change the value of #8FB7FF to whatever you like. http://www.color-hex.com

For your second request you’ll have to follow a couple of steps.
1. Install this plugin PHP Code Widget
2. Go back to Asteroid Options -> Custom CSS add this :

.blog-view > .entry-categories {
    display: none;
}

3. Also on Asteroid Options, go to Widget Areas tab. Check below excerpts. Save.
4. Go to WordPress widgets page. Add a PHP widget on the “Below Excerpts” area.
5. Add this code on the PHP widget :

<div class="entry-categories">
    <?php the_category(' '); ?>
</div>

Good luck,
Ron