Comments numbering

I am using the Travelify theme. I want to customise the Comments section of the posts.
I do not want the serial number of the comment to be shown.
I want the background of only the author comments to be changed to #eaeaea.

Is that possible by changing only the CSS?

Add this code to Theme Options - Other - Custom CSS

#content ol {
    list-style: none;
.bypostauthor article {
    background: #eaeaea;

You might want to add other styling to comments that you have made yourself but the basic idea is show above based on your description.