A few questions for my college newspaper’s new web site

My college’s newspaper is currently transferring everything over from CollegePublisher to WordPress for a publishing platform. I am currently in charge of designing/developing the new web site, but I don’t have too much PHP experience (which is where I need some help). I’ve been able to tweak the PHP in various pages to get some of the results I have wanted, but there are a few things I’m not too sure about because of the specific theme I am using. So lets start:

http://usmfreepress.org.s91716.gridserver.com/

1. Changing the order of the categories on the top nav bar. I’ve looked into this already and installed the ‘my category order’ plugin, but I don’t think it applies to this navbar (only for the sidebar widget). I’m trying to put it into an order of News, Pespectives, Arts, Sports, and so on. Since the plugin doesn’t seem to work for my theme, I was wondering if anyone could point to some specific code that would help me.

2. Organizing the hierarchy of posts by category.
You can see on the front page right now that the post order is by date, and what I want to do is have the first two columns always be posts from ‘News’, the second two from ‘Perspectives’, the third two from ‘Arts’, and the fourth from ‘Sports’. This may be a little complicated to pull off, but I was wondering if there was any solution for that.

3. Posting the date of the most recent edition on the top-right corner of the header. I want to have the date parallel with the categories and be a part of the nav bar. I’ve tried fiddling with the PHP file a little bit, but it’s come out unaligned with the categories. And I’d rather not have to update by coding in PHP every time. Is there a code that tells WordPress to grab the latest date of the last published article and display it?