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SEOMoz will find which page ranks for the term you are tracking, and you will be able to compare that.  So, yes, it will track your competitor's page.

First off, duplication doesn't matter.  Hopefully your title and slug are about the same topic.

That being said, my goal for the title is to be catchy, and my goal for the slug is to succinctly reflect that.  A basic practice you can do is take the title, remove the stop words, and that's your title.  No need to use words like the, in, on or a in a link.  Just adds unnecessary dashes, and makes it longer.  There's always exceptions to this, but in general this is what I practice for good results.

Latent dirichlet allocation is the newest school of thought on content: http://www.seomoz.org/blog/lda-and-googles-rankings-well-correlated

Essentially focusing on contextual clues to reinforce the idea of what a page is really about.

Writing about Jaguar the animal, talk about fur.  Writing about Jaguar the car, mention spark plugs.

Here's a followup article to SEOMoz's that's quite informative: http://www.seangolliher.com/2010/seo/185/

It get's into the actual math of the data.

It won't hurt your site if that's what you are asking.  Will it rank well?  Really depends on how your organic writing style relates to SEO.  Is it broke up into sections?  Do those sections of decent headers?  Are their pictures?  Are the pictures named appropriately?

The system works to identify the most relevant page to that keyword, and then grade it.  So, by not identifying your target page as the one associated with the keyword you have one of two problems:

1. Your appropriate page hasn't been indexed by the Moz Bot.

2. Your appropriate page isn't as relevant as that one.

If your website isn't being indexed properly then you need to adjust your internal linking.  If it is being indexed, then you need to take the steps to make your targeted page more relevant to the keyword.  Start with the URL, Title and H1.

Where's your server located?

Site size in itself is not a ranking factor.  Matt Cutts video on this exact topic: https://www.youtube.com/watch?v=AVOrml7fp2cThe benefit of additional pages is that you expand your opportunity for long tail traffic.  It also brings additional opportunities for links, assuming you write great content, and know how to distribute it properly.

Will it have a positive affect on your rankings?

Depends on your domains authority.  If you have one domain with a rocking link profile, and the others have almost none, then you would probably see a benefit.  If they are all equal, then you probably won't see any immediate impact.  However, if they are all equal, it would be easier to build links to one site rather than 5, 10 or 20.

The reasoning behind limiting the number of links is because the amount of authority that is passed by a page is divided by the total number of links on that page - regardless of nofollow or not.  So, the fewer links the more authority you are passing to each of those internal pages.  Answering your subsidiary question, there would be no SEO benefit from nofollowing these links.

That being said, usability trumps this in my book always.  Go into your Google Analytics, and see which of these links people are actually clicking.  If they are going into your drop down links, then leave them.  If they are only clicking on the head link, then consider chopping them.

Contact a webmaster that could use the link juice, and sell all the extra websites to them for a hefty sum?

The grading tool is used as a 10,000 foot view of the page.  It analyzes to the webpage to look for the proper usage of exact keyword phrases throughout the webpage.  It is not designed to analyze for synonyms or variations of keywords.

If you wanted to score a good grade for the variation you specified, then you would need to through that exact phrase in your Title, etc.  Keep in mind, though, the grading tool is not an indication of great SEO, just an indication that you have used keywords in the locations most highly correlated with positive results.

I've actually had this discussion a few times   My prime example is always The Telegraph who was SEO'd by Distilled (http://www.telegraph.co.uk/).  If you look at their menu structure they utilize submenus for each section to limit the number of links on a given page.  Granted, they have a massive amount of authority, but they are still trying to best harness how it passes through the website.

By clicking on 'World News' you get a sub-menu of different regions.  By clicking 'European News' you get another sub-menu for different countries/topics in Europe.

This allows you to pump as much authority as you can into your main topics, and makes sure that you have the most relevant links while in the sub-topics.

So, if ranking internal pages isn't important in your strategy, go ahead and forget about it.  However, if you want your deeper pages to rank well you should consider how reckless you are with your internal links.  You will be pleasantly surprised by the results.

Depends on how cute the cat is.

In the search box you will also want to search for the people you are targeting.  There isn't a universal search for people with 1 million followers, but you can use twitter search operatives to filter a lot.  There's some listed lower down on this page: http://mashable.com/2009/09/04/twitter-advanced-search/