1) WordPress.com blogs don't support plugins.
2) Your header is the blog title / header image area. What does headers (plural) mean?
3) The fact that you were seeing a similar line in both cases doesn't necessarily mean you apply the same coding. In this theme the line between the posts is a divider line while the line above each sidebar link is a top border to list items and the line below is a bottom border to the list. To remove those lines:
#sidebar .block ul, #sidebar .block li {
border: none;
}
PS I wonder why you chose Clean Home when you're leaving nothing of it.