Hey,
Let me just make sure I understand what you want. You want a page for each category, but instead of that page printing out the full content of all of the entries filed under that category, you just want those entries listed by title, right? So, say, you want a "Food" page, with a list of all the Food entries, and then a "Drink" page, with a list of all the Drink entries, and so on. Is that right?
If that's what you're looking for, then it sounds to me as if what you want
is a category archive -- just configured a little bit differently than the way the archives are configured by default in the MT templates.
You can get this to work by creating a new archive template and then mapping your category archives onto that new template.
By default, MT maps your category archives onto a template called "Entry Listing" -- which, despite its name, isn't really set up to do a simple listing at all.

So why not create a new one that is?
For example, for really
really simple list pages, you could just create a new archive template based on the Entry Listing template (copy and paste it, if you want), and then replace everything between the Header and the Footer with something like this:
CODE
<b>Entries filed under "<MTArchiveTitle>":</b>
<ul>
<MTEntries>
<li><a href="<MTEntryPermalink>"><MTEntryTitle></a></li>
</MTEntries>
</ul>
That would give you a very basic bulleted list of all of the entries filed under that category, linked to their Entry pages. You'd probably want to pretty it up a bit more, stick an h1 title in there somewhere, but you get the drift.
Once you've finished creating that new archive template, you'll want to make sure MT knows that it should map your category archives onto it, instead of onto the old template. Go into the edit screen for the old "Entry Listing" module. At the bottom of the screen, below the form where all the code goes, you'll see the Archive Mapping list. Delete the "Category" map from that template entirely. Then go to your new archive template and add the Category map to that one. Then republish, and you should be good to go.
For the "Popular Topics" list on the left side of the page...I assume mean you want it in the sidebar? There's a pre-made widget that ships with MT that I'm pretty sure does what you're looking for. I think it's called either "Categories" or "Category Archives." Something like that. You can find it in the Widget Templates.