1. The front page will only display the categories if a story in that category has been published. Makes sense to me because why would you browse a category if there isn't anything in it? I suggest manually promoting one story from each category via the admin to display all of your categories on the front page.
2. I am assuming that you are using the latest version of Mollio included with the nightly build 198. Open up templates/mollio-Beat/link_summary.tpl. Navigate to line 21. You will see this:
Code:
<a href="{$story_url}">{$title_short}</a>
replace with this:
Code:
<a href="{$url}">{$title_short}</a>
I "think" that should do the job. Let me know if it works.