Edit: partly resolved, I have the H1 in bold and H2 in italic, but I still don't have visible links at left.
I assume, then, that you're not too familiar with looking at sourcecode/using css - apologies if I'm overexplaining :o) !

If you look at the source code for your journal page (in Firefox), you can search for the content you want to format. I searched for "Archive" and can see it's contained in

<li class="module-list-item"><a href="http://alassenya.dreamwidth.org/calendar" class="archive">Archive</a></li>

The other links are contained in class="module-list-item" as well, so it makes sense to set the format for that class rather than "archive" (or for <li>, for that matter, since it may be used elsewhere). Specifically, you're formatting links, not text, contained within "module-list-item". Say you want links to be grey (sub your pretty purple colour):

.module-list-item a:link {color: #cccccc;} /* unvisited link */
.module-list-item a:visited {color: #cccccc;} /* visited link */
.module-list-item a:hover {color: #cccccc;} /* mouse over link */
.module-list-item a:active {color: #cccccc;} /* selected link */

As you can see, you can format visited/hover/active links differently.

Let me know if it works/you need more help :o)