Without having to change the coding, you can also change the images that you want to vanish into a spacer image, just save a blank, transparent 1x1 pixel as forum.png and topics.png and upload them to replace the existing images. The advantage to this is that 1. you aren't changing code - which helps for upgrades and 2. if you change your mind and want to add them in later, you can easily do so.
Here's where these are located:
- yoursite/modules/boonex/forum/layout/base/img/forum.png
- yoursite/modules/boonex/forum/layout/base_en/img/forum.png
- yoursite/modules/boonex/forum/layout/base/img/topic.png
- yoursite/modules/boonex/forum/layout/base_en/img/topic.png
Remember that if you are going to replace/overwrite an image, they go into your custom template folders along the same path: for example /templates/base/images/icons/ becomes /templates/your_template/images/icons/ folder (if you aren't using a custom template, you'll need to create one. This prevents problems when you upgrade)
As for the line, I believe that you'll find that in the main.css (modules/boonex/forum/layout/base/css/main.css and modules/boonex/forum/layout/base_en/css/main.css) around line 306:
.forum_table_list tr td {
border-top:1px solid #ccc;
}
Your color is probably different than #ccc as I've extensively altered my template, but the coding is the same. Change the above to:
.forum_table_list tr td {
border-top:0px
}
And your lines should vanish.