How do I remove the icons from the drop-down menu?

Here's instructions on how to remove the icons column from the home drop-down menu sub-options.

In the themes & layouts area edit the layout for the page (obviously you'll need to repeat this process for every layout).
At the bottom of the page add a new "article" component.
Edit the settings for this new component - set the margins to "0", make sure the header and footer options are unchecked and make sure the transparent background option is checked.
Select the "HTML (advanced)" option and paste the following text into the text box:

<style>.t_iconcol {display:none;}</style>
Click OK, save the modified layout and you should be good to go!